{"id":229,"date":"2023-07-10T21:50:05","date_gmt":"2023-07-10T21:50:05","guid":{"rendered":"https:\/\/mathority.org\/id\/contoh-kedudukan-relatif-dua-garis-pada-bidang-kartesius-2d-r2\/"},"modified":"2023-07-10T21:50:05","modified_gmt":"2023-07-10T21:50:05","slug":"contoh-kedudukan-relatif-dua-garis-pada-bidang-kartesius-2d-r2","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/contoh-kedudukan-relatif-dua-garis-pada-bidang-kartesius-2d-r2\/","title":{"rendered":"Posisi relatif dua garis pada bidang"},"content":{"rendered":"<p>Di halaman ini Anda akan menemukan penjelasan berbagai metode yang ada untuk menentukan posisi relatif dua garis pada bidang (di R2). Selain itu, Anda akan melihat beberapa contoh dan Anda akan dapat berlatih dengan latihan yang diselesaikan langkah demi langkah. <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-104\"><\/div>\n<\/div>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcual-es-la-posicion-relativa-de-dos-rectas-en-el-plano\"><\/span> Berapakah kedudukan relatif dua garis pada bidang tersebut? <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-105\"><\/div>\n<\/div>\n<p> Sebelum melihat posisi relatif antara dua garis pada suatu bidang, tentunya anda perlu mengetahui secara pasti apa itu garis, hal tersebut dapat anda temukan pada <a href=\"https:\/\/mathority.org\/id\/pengertian-ciri-ciri-garis-contoh-jenis-garis-lurus\/\">definisi garis<\/a> .<\/p>\n<p> Jadi, ketika bekerja dalam dua dimensi (dalam R2), ada 3 jenis kemungkinan posisi relatif antara dua garis: <\/p>\n<div class=\"wp-block-columns is-layout-flex wp-container-136\">\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#ff6f00\"> <strong>garis-garis yang berpotongan<\/strong> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/angles-droits-secants.webp\" alt=\"kedudukan relatif dua garis yang berpotongan\" class=\"wp-image-1644\" width=\"205\" height=\"192\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Dua garis yang berpotongan hanya mempunyai satu titik yang sama. <\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#ff6f00\"> <strong><strong>Garis sejajar<\/strong><\/strong> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/droites-paralleles-a-langle.webp\" alt=\"posisi relatif garis sejajar\" width=\"209\" height=\"189\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Dua garis dikatakan sejajar jika tidak mempunyai titik persekutuan. Artinya, jika mereka tidak pernah berpapasan. <\/p>\n<\/div>\n<div class=\"wp-block-column is-layout-flow\">\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#ff6f00\"> <strong>garis yang bertepatan<\/strong> <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/angle-coincident-lignes.webp\" alt=\"posisi relatif dari garis-garis yang berhimpitan\" width=\"189\" height=\"168\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Dua garis dikatakan sama jika semua titiknya sama. <\/p>\n<\/div>\n<\/div>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-106\"><\/div>\n<\/div>\n<p> Sebaliknya, sudut antara dua garis pada bidang juga bergantung pada posisi relatifnya:<\/p>\n<ul>\n<li> Garis berpotongan berpotongan pada sudut antara 0\u00ba (tidak termasuk) dan 90\u00ba (inklusif). Selain itu, jika membentuk sudut siku-siku 90\u00ba saja, berarti kedua garis tersebut tegak lurus.<\/li>\n<li> Garis sejajar membentuk sudut 0\u00ba karena arahnya sama.<\/li>\n<li> Dan, untuk alasan yang sama, garis-garis yang berhimpitan juga membentuk sudut 0\u00ba di antara keduanya.<\/li>\n<\/ul>\n<p> Jika Anda ingin mengetahui cara menghitung sudut antara dua garis, Anda bisa melihat <a href=\"https:\/\/mathority.org\/id\/sudut-antara-dua-garis-contoh-rumus-menyelesaikan-latihan-vektor-pengarah-lereng\/\">rumus sudut antara dua garis<\/a> . Di sini Anda akan menemukan penjelasan detail tentang cara menentukan sudut antara dua garis, serta beberapa contoh bahkan latihan soal agar Anda dapat berlatih dan memahami konsepnya secara maksimal. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-hallar-la-posicion-relativa-de-dos-rectas-en-el-plano\"><\/span>Cara mencari kedudukan relatif dua garis pada bidang <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-109\"><\/div>\n<\/div>\n<p> Mengetahui posisi relatif antara dua garis dalam ruang dua dimensi bergantung pada cara garis tersebut dinyatakan:<\/p>\n<ul>\n<li> <strong>Vektor arah garis:<\/strong> jika dua garis mempunyai vektor arah yang berbeda, maka keduanya harus berpotongan. Sebaliknya, jika koordinat vektor arahnya sama atau sebanding, keduanya bisa sejajar atau berimpit (perlu diperiksa apakah keduanya mempunyai titik yang sama).<\/li>\n<\/ul>\n<ul>\n<li> <strong>Persamaan eksplisit:<\/strong> ketika dua garis mempunyai kemiringan yang berbeda\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cbf220caa0234311cbdde7c24a842b1b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(m)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"28\" style=\"vertical-align: -5px;\"><\/p>\n<p> mereka mengering Sebaliknya jika garis mempunyai kemiringan yang sama tetapi urutannya berbeda di titik asal<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9098105a2659ae64387c39c113fab615_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(n)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"23\" style=\"vertical-align: -5px;\"><\/p>\n<p> mereka paralel. Terakhir, dua garis tertukar padahal awalnya mempunyai kemiringan dan ordinat yang sama.<\/li>\n<\/ul>\n<ul>\n<li> <strong>Persamaan umum (atau implisit):<\/strong> dua garis dengan koefisien nonproporsional A dan B akan selalu berpotongan. Akan tetapi, ketiga suku tersebut akan sejajar jika kedua parameter tersebut sebanding satu sama lain tetapi tidak sebanding dengan koefisien C. Dan, terakhir, jika ketiga suku tersebut sebanding, hal ini berarti garis-garis tersebut tertukar.<\/li>\n<\/ul>\n<p> Jika anda masih ragu dengan persamaan garis di atas, anda bisa membaca penjelasan <a href=\"https:\/\/mathority.org\/id\/persamaan-garis-semua-rumus-contoh-latihan-yang-diselesaikan\/\">persamaan garis pada bidang<\/a> . Di sini Anda akan menemukan rumus semua persamaan garis, cara menghitungnya, contoh dan latihan penyelesaian persamaan garis.<\/p>\n<p> Dalam tabel berikut Anda memiliki ringkasan properti sebelumnya: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/position-relative-de-deux-droites-dans-le-plan-1.webp\" alt=\"posisi relatif dua garis pada bidang\" class=\"wp-image-1718\" width=\"675\" height=\"403\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p> Selanjutnya, kita akan melihat dua contoh cara menentukan posisi relatif antara dua garis:<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-1\"><\/span> Contoh 1<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li> Temukan posisi relatif antara dua garis berikut yang didefinisikan dalam bentuk persamaan eksplisit:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-da7047627c75c1e890b8dcd638f77ed6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r: \\ y=3x+2 \\qquad \\qquad s: \\ y=3x-4\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"294\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Kedua garis mempunyai kemiringan yang sama:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-873fd0b2da446bff0d72d56424846ad5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m_r = m_s = 3\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"102\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p> Tetapi mereka memiliki komputer yang berbeda pada awalnya:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dd55fdc8ff8e806fd683fad5ee625dc3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_r =2\\neq n_s=-4\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"139\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Jadi, karena kemiringannya sama tetapi titik potongnya berbeda, <strong>maka garis-garis tersebut sejajar<\/strong> .<\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-2\"><\/span> Contoh 2<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li> Tentukan posisi relatif antara dua garis berikut yang dinyatakan dengan persamaan implisit (atau umum):<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c917d50b692b0f59a5846479d74b6e19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r: \\ 4x+2y-6=0 \\qquad \\qquad s: \\ -2x-y+3=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"378\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Kedua garis dinyatakan sebagai persamaan eksplisit, oleh karena itu kita perlu melihat apakah ada koefisien yang sebanding:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-cce65e5ed8b8969e9349325d13a192ec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{4}{-2}=\\cfrac{2}{-1} = \\cfrac{-6}{3} = -2\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"173\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Ketiga suku garis tersebut sebanding, jadi <strong>kedua garis tersebut berimpit<\/strong> . <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"determinar-la-posicion-relativa-de-dos-rectas-en-el-plano-con-un-sistema-de-ecuaciones\"><\/span> Tentukan kedudukan relatif dua garis pada bidang dengan sistem persamaan<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Cara lain untuk mengetahui posisi relatif antara dua garis adalah dengan menganalisis sistem persamaan yang dibentuk oleh persamaan garis:<\/p>\n<ul>\n<li> Jika <strong>sistem mempunyai solusi unik<\/strong> , garis-garisnya berpotongan. Selanjutnya titik potong kedua garis tersebut merupakan penyelesaian sistem.<\/li>\n<li> Jika suatu <strong>sistem tidak mempunyai penyelesaian<\/strong> , hal ini menunjukkan bahwa garis-garis tersebut tidak mempunyai titik-titik yang sama sehingga merupakan garis-garis sejajar.<\/li>\n<li> Jika <strong>sistem mempunyai solusi yang tak terhingga banyaknya<\/strong> , ini berarti semua garis mempunyai titik-titik yang sama dan oleh karena itu merupakan garis-garis yang berpotongan.<\/li>\n<\/ul>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-3\"><\/span> Contoh 3<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li> Hitung posisi relatif dua garis berikut dengan menggunakan sistem persamaan:<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a333dd2d8363e9caf5bfcb7fcc4b307a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r: \\ 3x+4y+5=0 \\qquad \\qquad s: \\ 5x+y-3=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"364\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Untuk mencari posisi relatif kedua garis, kita perlu menyelesaikan sistem persamaan linear yang dibentuk oleh kedua garis berikut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-243b1e787e6532fbafbfca53d934f4ad_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left.\\begin{array}{l} 3x+4y+5=0\\\\[2ex] 5x+y-3=0\\end{array}\\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"143\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Dalam hal ini kita akan menyelesaikan sistem tersebut dengan metode substitusi. Oleh karena itu kami akan mengisolasi variabel tersebut<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> dari persamaan kedua dan substitusikan ke persamaan pertama: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ad3456c92c838f40d60afdb45e1eb2f3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left.\\begin{array}{l} 3x+4y+5=0\\\\[2ex] 5x+y-3=0\\end{array}\\right\\} \\begin{array}{l} \\\\[2ex] \\longrightarrow \\ y=3-5x \\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"279\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e878bb5de718162dd547d349041c5a17_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3x+4(3-5x)+5=0\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"176\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b44339147102246aa99ce775ae1f4415_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3x+12-20x+5=0\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"171\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e51763736cd6ea39f0cf08f9c8d067f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3x-20x=-12-5\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"153\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-55630337168997a6a2a76aeaef1ad669_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-17x=-17\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"96\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-50540499fd4810f10aa8d48376dc8370_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\cfrac{-17}{-17} = 1\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"107\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Dan begitu kita tahu betapa berharganya hal yang tidak diketahui itu<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> Kami mengganti nilainya ke dalam ekspresi yang ditemukan <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-526e84c5b87e970b9045246e059785fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"18\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b53c99a78c482f7c71588f8e0d769e9b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=3-5x \\ \\xrightarrow{x \\ = \\ 1} \\ y = 3 -5\\cdot 1\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"245\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9985617b47dec6ac0faa8d98665cd8b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y = 3 -5 = -2\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"118\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Oleh karena itu kita hanya memperoleh satu penyelesaian dari sistem persamaan yang terdiri dari dua garis tersebut, sehingga <strong>kedua garis tersebut berpotongan<\/strong> . Dan titik perpotongannya adalah solusi sistem, yaitu titik <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d9dbd776d7ff2a9a72963326b278e12b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(1,-2).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"57\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-posicion-relativa-de-dos-rectas-en-el-plano\"><\/span> Menyelesaikan masalah kedudukan relatif dua garis pada bidang<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> Latihan 1<\/h3>\n<p> Tentukan apakah garis-garis berikut berpotongan, sejajar, atau berimpit: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d8857a4b8101efdfb88107fae20a16bb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r: \\ 3x-y+4=0 \\qquad \\qquad s: \\ 9x-3y+3=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"364\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>lihat solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Kedua garis dinyatakan sebagai persamaan implisit (atau umum), oleh karena itu kita perlu melihat apakah ada koefisien yang proporsional:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1fd9a2de250f3a5cb1a7025e30eb00b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{3}{9}=\\cfrac{-1}{-3} \\neq \\cfrac{4}{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"99\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Hanya koefisien A dan B pada garis-garis yang sebanding satu sama lain, dan tidak sebanding dengan koefisien C. Oleh karena itu <strong>, kedua garis tersebut sejajar<\/strong> .<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\"> Latihan 2<\/h3>\n<p> Temukan posisi relatif antara dua garis berikut yang dinyatakan sebagai persamaan parametrik: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-bafb951a2141722b0bbb7a1681f506ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle r: \\ \\begin{cases} x=4-5t \\\\[2ex] y= 1+3t \\end{cases}\\qquad \\qquad s: \\ \\begin{cases} x=-2t \\\\[2ex] y=6+9t \\end{cases}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"341\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>lihat solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Kita dapat menyelesaikan sistem persamaan yang dibentuk oleh dua garis untuk mencari posisi relatifnya. Namun karena berbentuk persamaan parametrik, vektor arahnya dapat dengan mudah dicari dan jika tidak proporsional berarti garis-garisnya berpotongan. Dan dalam hal ini, kita tidak akan menghabiskan banyak waktu untuk menyelesaikan keseluruhan sistem persamaan.<\/p>\n<p class=\"has-text-align-left\"> Sehingga koordinat kartesius vektor arah tiap garis adalah angka di depan parameternya <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-40f8b062c79839dcf7f2885a9e1469e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"t:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2428dfdbfe571940b2c02da2581f3c83_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{r} =(-5,3) \\qquad \\qquad \\vv{s}=(-2,9)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"241\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Setelah kita mengetahui vektor arahnya, kita periksa proporsionalitasnya:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-38d5cefd7229992008378fea28376585_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{-5}{-2} \\neq \\cfrac{3}{9}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"65\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Vektor-vektor arahnya tidak sebanding, oleh karena itu <strong>garis-garisnya saling bersilangan<\/strong> .<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\"> Latihan 3<\/h3>\n<p> Tunjukkan apakah garis-garis berikut berpotongan, sejajar atau berhimpitan dan temukan juga titik potong di antara keduanya (jika ada). <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9e1c8f120a7d86580808425ce4452bbc_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r: \\ y=4x-5 \\qquad \\qquad s: \\ y=-2x+7\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"308\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>lihat solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Kedua garis tersebut ditentukan oleh persamaan eksplisitnya dan memiliki kemiringan yang berbeda:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5f8ff0ff270ad51df36633f3a7da08f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m_r =4 \\neq m_s = -2\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"147\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Karena kemiringannya berbeda, <strong>garis-garisnya berpotongan<\/strong> .<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, karena garis-garis tersebut berpotongan maka keduanya akan mempunyai 1 titik persekutuan dan untuk menghitungnya kita harus menyelesaikan sistem persamaan yang dibentuk oleh kedua garis tersebut:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b3923ff74a214543ddd2cc44a42e3813_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left.\\begin{array}{l} y=4x-5\\\\[2ex] y=-2x+7\\end{array}\\right\\}\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"117\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dalam hal ini kita akan menyelesaikan sistem dengan metode pemerataan karena keduanya<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> sudah dihapus: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1043bcfc74c9c720f4d738403a0a5de9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"42\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-30260dd1609f72d1b91e2431be1c4fec_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4x-5=-2x+7\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"137\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-13a0532699efab3ce3fa0565ddd295f0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4x+2x=5+7\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"123\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-20e2c2528083b16701309669036284a5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6x=12\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"60\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-54e0507e23104e014591f7bb9d0b9e02_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=\\cfrac{12}{6} = 2\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"85\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan begitu kita menghadapi hal yang tidak diketahui<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ede05c264bba0eda080918aaa09c4658_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"10\" style=\"vertical-align: 0px;\"><\/p>\n<p> kami mengganti nilainya dengan ekspresi apa pun<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0af556714940c351c933bba8cf840796_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: -4px;\"><\/p>\n<p> untuk mengetahui berapa nilainya: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fa1fe37c29ef252a2729d235c875f0ee_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=4x-5\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"82\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e2858c9e13db1ef7d1777f6ee50501ae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y = 4\\cdot 2 -5 = 8 -5 = 3\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"190\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Jadi titik potong kedua garis tersebut merupakan hasil sistem : <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-786ded60a053402b1fedabd27477fa77_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{(2,3)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"38\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Latihan 4<\/h3>\n<p> Hitung nilai yang tidak diketahui<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> Dan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> sehingga dua garis berikut sejajar: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-22406447457807bd671683c76d717494_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r: \\ 2x-4y+6=0 \\qquad \\qquad s: \\ x+ay+b=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"363\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>lihat solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Garis-garis tersebut dijelaskan dalam bentuk persamaan umum (atau implisit). Oleh karena itu, agar kedua garis sejajar maka koefisien A dan Bnya harus proporsional, yaitu persamaan berikut harus dipenuhi:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-426cf79f7967a39d05301b57327425b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{2}{1} = \\cfrac{-4}{a}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"65\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu kita harus menyelesaikan persamaan sebelumnya untuk mendapatkan nilai yang tidak diketahui<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2ebc59bdf10d3d739bfa532b65c85287_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"13\" style=\"vertical-align: 0px;\"><\/p>\n<p> Untuk melakukan ini, kita mengalikan pecahan secara melintang: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-778399973685974e5fab6ef86a4ff316_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2 \\cdot a = -4 \\cdot 1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"98\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fa72e494965cde5a39eef1003b449a40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a = \\cfrac{-4}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"66\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-115c97df060d69970606b1ae494bb4b9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{a=-2}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"55\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sebaliknya, agar garis-garis sejajar, suku-suku independennya tidak dapat sebanding dengan koefisien lainnya:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0eee380a4c98c2379e3b88fb5c00038e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{2}{1} \\neq \\cfrac{6}{b}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"43\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, seperti sebelumnya, kita menyelesaikan pertidaksamaan dengan mengalikan pecahan secara melintang: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e8f6fbac3664ac51fabbd88c63a6265c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2 \\cdot b \\neq 6 \\cdot 1\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"83\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0d382f6f8b7a55e13812975129a29da1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b \\neq \\cfrac{6}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"42\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b74bf2f543632f7b7adec4ebd1f59b0e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{b\\neq 3}\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"40\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Singkatnya, agar kedua garis tersebut sejajar<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-5c53d6ebabdbcfa4e107550ea60b1b19_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"a\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> harus 2 dan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f56d50c26583f9a035ff6b4e3c0ca5c0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"b\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> dapat berupa bilangan real apa pun kecuali 3.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\"> Latihan 5<\/h3>\n<p> Temukan persamaan eksplisit garis yang sejajar dengan garis tersebut<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> dan apa yang terjadi di titik tersebut<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f3beed6e0b45d9e34dfb895ea2711797_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(3,-1).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"71\" style=\"vertical-align: -5px;\"><\/p>\n<p> menjadi lurus <\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c5986f031932e6b3512dc564514c34b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r:\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"17\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-731b64c6b0926aa016c615182da3d7d3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r: \\; y=2x+5\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"110\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-start otfm-sp__wrapper otfm-sp__box js-otfm-sp-box__closed otfm-sp__E4F0FE\" role=\"button\" tabindex=\"0\" aria-expanded=\"false\" data-otfm-spc=\"#E4F0FE\" style=\"text-align:center\">\n<div class=\"otfm-sp__title\"> <strong>lihat solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Sehingga garis tersebut sejajar dengan garis<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-42ca8c420951296e93092e708435813a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r,\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"12\" style=\"vertical-align: -4px;\"><\/p>\n<p> keduanya harus mempunyai kemiringan yang sama. dan kemiringan garis<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-c409433a9e2dfcdb83360a974d243f18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> adalah 2:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-f3439899d4781058b8eb19021ac25e27_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m = 2\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"47\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, persamaan garis yang perlu kita cari adalah:<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1bbbc8cea82d1688f21bcabc8ef7fa3e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=2x+n\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"85\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan setelah kita mengetahui kemiringan garis, kita dapat menghitung perpotongan y dengan mensubstitusikan titik yang termasuk dalam garis tersebut ke dalam persamaan garis: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-e83b6065f321642320b736c8b866043c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(3,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"66\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-826526b2aef06a1f04f17c54f8db7369_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y= 2x+n \\ \\xrightarrow{x=3 \\ ; \\ y=-1} \\ -1=2\\cdot 3 +n\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"303\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-0aba6175b45d89611019ec5f89ebd82f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-1=6+ n\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"87\" style=\"vertical-align: -2px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-afeec8d1085931aed83404a8a7ba45dd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-1-6= n\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"87\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-35b29a0fad2239bd507e2d044f846092_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-7= n\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"56\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Jadi persamaan garisnya secara eksplisit adalah: <\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-fd88ac415e522e13e3437bb0e3da393a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{y=2x-7}\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"83\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<p> Jika Anda sudah sampai sejauh ini, berarti Anda sudah menguasai posisi relatif antara dua garis dalam denah. Bagus sekali!<\/p>\n<p> Namun satu hal yang membuat banyak orang bertanya-tanya adalah&#8230;dan apa gunanya mengetahui posisi relatif antara dua garis?<\/p>\n<p> Nah, salah satu penerapan posisi relatif antar garis adalah untuk dapat mengetahui jarak antara 2 garis, karena perhitungan jarak dua garis bergantung pada posisi relatifnya:<\/p>\n<ul>\n<li> Jika garis-garis tersebut berpotongan atau berimpit maka jaraknya nol.<\/li>\n<li> Sebaliknya, jika garisnya sejajar, rumus tertentu harus diterapkan. Jika Anda lebih tertarik, Anda bisa melihat cara menghitung <a href=\"https:\/\/mathority.org\/id\/jarak-antara-dua-garis-sejajar-contoh-rumus-latihan-soal-yang-diselesaikan\/\">jarak antara dua garis sejajar<\/a> .<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Di halaman ini Anda akan menemukan penjelasan berbagai metode yang ada untuk menentukan posisi relatif dua garis pada bidang (di R2). Selain itu, Anda akan melihat beberapa contoh dan Anda akan dapat berlatih dengan latihan yang diselesaikan langkah demi langkah. Berapakah kedudukan relatif dua garis pada bidang tersebut? Sebelum melihat posisi relatif antara dua garis &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/contoh-kedudukan-relatif-dua-garis-pada-bidang-kartesius-2d-r2\/\"> <span class=\"screen-reader-text\">Posisi relatif dua garis pada bidang<\/span> Selengkapnya &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[47],"tags":[],"class_list":["post-229","post","type-post","status-publish","format-standard","hentry","category-titik-garis-dan-bidang"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Posisi relatif dua garis pada bidang - Mathority<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathority.org\/id\/contoh-kedudukan-relatif-dua-garis-pada-bidang-kartesius-2d-r2\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Posisi relatif dua garis pada bidang - Mathority\" \/>\n<meta property=\"og:description\" content=\"Di halaman ini Anda akan menemukan penjelasan berbagai metode yang ada untuk menentukan posisi relatif dua garis pada bidang (di R2). Selain itu, Anda akan melihat beberapa contoh dan Anda akan dapat berlatih dengan latihan yang diselesaikan langkah demi langkah. Berapakah kedudukan relatif dua garis pada bidang tersebut? Sebelum melihat posisi relatif antara dua garis &hellip; Posisi relatif dua garis pada bidang Selengkapnya &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/id\/contoh-kedudukan-relatif-dua-garis-pada-bidang-kartesius-2d-r2\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-10T21:50:05+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/angles-droits-secants.webp\" \/>\n<meta name=\"author\" content=\"Tim Mathority\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Ditulis oleh\" \/>\n\t<meta name=\"twitter:data1\" content=\"Tim Mathority\" \/>\n\t<meta name=\"twitter:label2\" content=\"Estimasi waktu membaca\" \/>\n\t<meta name=\"twitter:data2\" content=\"6 menit\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathority.org\/id\/contoh-kedudukan-relatif-dua-garis-pada-bidang-kartesius-2d-r2\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/id\/contoh-kedudukan-relatif-dua-garis-pada-bidang-kartesius-2d-r2\/\"},\"author\":{\"name\":\"Tim Mathority\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38\"},\"headline\":\"Posisi relatif dua garis pada bidang\",\"datePublished\":\"2023-07-10T21:50:05+00:00\",\"dateModified\":\"2023-07-10T21:50:05+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/id\/contoh-kedudukan-relatif-dua-garis-pada-bidang-kartesius-2d-r2\/\"},\"wordCount\":1254,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathority.org\/id\/#organization\"},\"articleSection\":[\"Titik, garis, dan bidang\"],\"inLanguage\":\"id\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathority.org\/id\/contoh-kedudukan-relatif-dua-garis-pada-bidang-kartesius-2d-r2\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/id\/contoh-kedudukan-relatif-dua-garis-pada-bidang-kartesius-2d-r2\/\",\"url\":\"https:\/\/mathority.org\/id\/contoh-kedudukan-relatif-dua-garis-pada-bidang-kartesius-2d-r2\/\",\"name\":\"Posisi relatif dua garis pada bidang - 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Selain itu, Anda akan melihat beberapa contoh dan Anda akan dapat berlatih dengan latihan yang diselesaikan langkah demi langkah. Berapakah kedudukan relatif dua garis pada bidang tersebut? Sebelum melihat posisi relatif antara dua garis &hellip; Posisi relatif dua garis pada bidang Selengkapnya &raquo;","og_url":"https:\/\/mathority.org\/id\/contoh-kedudukan-relatif-dua-garis-pada-bidang-kartesius-2d-r2\/","article_published_time":"2023-07-10T21:50:05+00:00","og_image":[{"url":"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/angles-droits-secants.webp"}],"author":"Tim Mathority","twitter_card":"summary_large_image","twitter_misc":{"Ditulis oleh":"Tim Mathority","Estimasi waktu membaca":"6 menit"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathority.org\/id\/contoh-kedudukan-relatif-dua-garis-pada-bidang-kartesius-2d-r2\/#article","isPartOf":{"@id":"https:\/\/mathority.org\/id\/contoh-kedudukan-relatif-dua-garis-pada-bidang-kartesius-2d-r2\/"},"author":{"name":"Tim Mathority","@id":"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38"},"headline":"Posisi relatif dua garis pada bidang","datePublished":"2023-07-10T21:50:05+00:00","dateModified":"2023-07-10T21:50:05+00:00","mainEntityOfPage":{"@id":"https:\/\/mathority.org\/id\/contoh-kedudukan-relatif-dua-garis-pada-bidang-kartesius-2d-r2\/"},"wordCount":1254,"commentCount":0,"publisher":{"@id":"https:\/\/mathority.org\/id\/#organization"},"articleSection":["Titik, garis, dan bidang"],"inLanguage":"id","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathority.org\/id\/contoh-kedudukan-relatif-dua-garis-pada-bidang-kartesius-2d-r2\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathority.org\/id\/contoh-kedudukan-relatif-dua-garis-pada-bidang-kartesius-2d-r2\/","url":"https:\/\/mathority.org\/id\/contoh-kedudukan-relatif-dua-garis-pada-bidang-kartesius-2d-r2\/","name":"Posisi relatif dua garis pada bidang - 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