{"id":231,"date":"2023-07-10T20:47:48","date_gmt":"2023-07-10T20:47:48","guid":{"rendered":"https:\/\/mathority.org\/id\/pengertian-garis-sejajar-dan-contohnya\/"},"modified":"2023-07-10T20:47:48","modified_gmt":"2023-07-10T20:47:48","slug":"pengertian-garis-sejajar-dan-contohnya","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/pengertian-garis-sejajar-dan-contohnya\/","title":{"rendered":"Garis sejajar"},"content":{"rendered":"<p>Di sini Anda akan menemukan segala sesuatu tentang garis sejajar: apa artinya, cara menentukan apakah dua garis sejajar, sifat-sifatnya, dll. Selain itu, Anda akan dapat melihat beberapa contoh dan penyelesaian latihan garis sejajar. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfque-son-las-rectas-paralelas\"><\/span> Apa itu garis sejajar?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Garis sejajar adalah garis yang tidak pernah berpotongan, artinya meskipun lintasannya diperpanjang hingga tak terhingga, garis tersebut tidak akan pernah bersentuhan satu sama lain.<\/strong> Oleh karena itu, titik-titik pada dua garis sejajar selalu berjarak sama satu sama lain, dan terlebih lagi, dua garis sejajar tidak mempunyai titik yang sama.<\/p>\n<p> Misalnya, dua garis berikut ini sejajar: <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/droites-paralleles-a-langle.webp\" alt=\"apa itu garis sejajar\" class=\"wp-image-1643\" width=\"212\" height=\"191\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Secara umum kita menunjukkan bahwa dua garis sejajar dengan 2 batang vertikal || yang tersirat<\/p>\n<p> Sebaliknya, meskipun dua garis sejajar tidak pernah berpotongan, dalam geometri analitik dikatakan keduanya membentuk sudut 0\u00ba karena arahnya sama. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"%c2%bfcuando-dos-rectas-son-paralelas\"><\/span> Kapan dua garis sejajar?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Setelah kita mengetahui pengertian garis sejajar, kita akan mengetahui cara mencari dua garis sejajar. Tentu saja salah satu caranya adalah dengan membuat grafik garis-garis tersebut dan melihat apakah garis-garis tersebut berpotongan pada grafik, namun ada metode yang lebih sederhana dan mudah digunakan. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"determinar-el-paralelismo-de-dos-rectas-con-sus-pendientes\"><\/span>Tentukan kesejajaran dua garis dengan gradiennya<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Anda dapat mengetahui letak dua garis sejajar dengan melihat kemiringan setiap garis. Ingatlah bahwa kemiringan suatu garis adalah 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-6b41df788161942c6f98604d37de8098_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"15\" style=\"vertical-align: 0px;\"><\/p>\n<p> dari persamaan eksplisit dan persamaan titik-kemiringan 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-554535c3d25b9adc547adff39b691f65_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=mx+n \\qquad \\qquad y-y_0=m(x-x_0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"311\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Namun ada beberapa cara untuk menentukan kemiringan suatu garis, maka untuk mengetahui cara menghitungnya, kami sarankan untuk melihat <a href=\"https:\/\/mathority.org\/id\/kemiringan-rumus-garis\/\">rumus kemiringan suatu garis<\/a> . Selain itu, pada halaman tertaut Anda juga akan menemukan penjelasan tentang apa yang diwakili oleh kemiringan suatu garis dan mengapa hal itu sangat penting bagi sebuah garis.<\/p>\n<p> Jadi, pada suatu bidang, <strong>dua garis dikatakan sejajar jika mempunyai kemiringan (koefisien m) yang sama<\/strong> <strong>dan ordinat yang berbeda di titik asal<\/strong> (koefisien n) <strong>.<\/strong><\/p>\n<p> Misalnya, dua garis berikut ini 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-9c3b90bedb2e4cabf5abbe2e1503a297_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r: \\ y=5x+1 \\qquad \\qquad s: \\ y=5x-3\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"294\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Kedua garis tersebut merupakan dua garis sejajar karena keduanya mempunyai kemiringan yang sama dan terlebih lagi suku-suku bebasnya 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-38578bc1ef19827cb3e3979a1320c2b8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m_r =m_s =5\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"101\" style=\"vertical-align: -3px;\"><\/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-16a05a21fe1359e991a46663d98f9cfa_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"n_r =1 \\neq n_s =-3\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"139\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Perlu dicatat bahwa jika dua garis memiliki kemiringan yang sama dan pada saat yang sama komputer yang sama berada di titik asal, maka kedua garis tersebut akan menjadi <strong>garis yang identik<\/strong> karena keduanya akan persis sama. <\/p>\n<h3 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"hallar-el-paralelismo-de-dos-rectas-a-partir-de-la-ecuacion-implicita\"><\/span> Temukan paralelisme dua garis dari persamaan implisit<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p> Ingatlah bahwa persamaan garis implisit (atau umum) 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-02f4d03229cc8bd79a81b676a8132f37_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"Ax+By+C=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"137\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Jadi, <strong>jika koefisien A dan B dua garis sebanding satu sama lain tetapi tidak sebanding dengan koefisien C<\/strong> , berarti 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-ce8e0c71142b89e0985aa730b40f15db_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r: \\ Ax+By+C=0 \\qquad \\qquad s: \\ A'x+B'y+C'=0\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"417\" 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-b71b3ef6225dee8ab67d4cb0586d2eb6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{A}{A'} = \\cfrac{B}{B'} \\neq \\cfrac{C}{C'} \\quad \\bm{\\longrightarrow} \\quad r \\parallel s\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"206\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Berikut dua garis sejajar yang dinyatakan dalam bentuk persamaan umum (atau implisit):<\/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-933c8de113e41643cb6d90ee628a7647_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r: \\ 4x-6y+7=0 \\qquad \\qquad s: \\ -2x+3y-1=0\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"387\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Mereka sejajar karena angka-angka di depan variabel<\/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> sebanding dengan angka di depan variabel<\/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> , tetapi tidak dengan persyaratan independen.<\/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-883f961c4fb1d1a5077360ddf3a83add_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{4}{-2} = \\cfrac{-6}{3} = -2 \\neq \\cfrac{7}{-1}=-7\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"220\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Seperti sebelumnya, jika semua koefisien (A, B, dan C) dari dua garis implisit adalah proporsional, hal ini berarti kedua garis tersebut berimpit, atau dengan kata lain keduanya sama besar. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"propiedades-de-las-rectas-paralelas\"><\/span> Sifat-sifat garis sejajar<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Ciri-ciri garis sejajar adalah sebagai berikut:<\/p>\n<ul>\n<li> <strong>Sifat simetris<\/strong> : jika suatu garis sejajar dengan garis lainnya, maka garis tersebut juga sejajar dengan garis pertama. Sifat ini juga dimiliki oleh garis tegak lurus.<\/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-cde8c90b403c06e960548aa1ae07838e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r \\parallel s \\ \\longrightarrow \\ s \\parallel r\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"121\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> <strong>Sifat transitif<\/strong> : jika suatu garis sejajar dengan garis lain, dan garis kedua sejajar dengan garis ketiga, maka garis pertama juga sejajar dengan garis ketiga.<\/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-d8ed30d043440defc6ebfd30c740e937_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\left. \\begin{array}{c} r \\parallel s\\\\[2ex] s \\parallel q \\end{array} \\right\\} \\longrightarrow \\ r \\parallel q\" title=\"Rendered by QuickLaTeX.com\" height=\"65\" width=\"139\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li> <strong>Hasil kali skalar<\/strong> vektor-vektor arah (vektor yang menunjukkan arah suatu garis) dari dua garis sejajar sama dengan hasil kali modul-modulnya.<\/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-dc62cec1dba854bf4f122a3a258615b6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r \\parallel s \\ \\longrightarrow \\ \\vv{\\text{v}}_r \\cdot \\vv{\\text{v}}_s= \\lvert \\vv{\\text{v}}_r \\rvert \\cdot \\lvert \\vv{\\text{v}}_s \\rvert\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"219\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<ul>\n<li> Selain itu, vektor arah dua garis sejajar selalu bergantung linier satu sama lain karena <strong>proporsional<\/strong> .<\/li>\n<\/ul>\n<p> Kondisi ini diperlukan agar garis sejajar tetapi tidak cukup, atau dengan kata lain, dua garis sejajar harus mempunyai vektor arah yang sebanding, tetapi kenyataan bahwa dua garis mempunyai vektor arah yang sebanding tidak secara langsung berarti bahwa kedua garis tersebut sejajar. Karena garis-garis yang berhimpitan juga mempunyai vektor-vektor arah yang sebanding.<\/p>\n<ul>\n<li> Garis yang sejajar sumbu absis (sumbu X) bersifat horizontal dan selalu berbentuk\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-afa765d3f555400c4f5b69f3a3d3d4a2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=k.\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"47\" style=\"vertical-align: -4px;\"><\/p>\n<\/li>\n<\/ul>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/lignes-paralleles-axe-x.webp\" alt=\"garis lurus sejajar dengan sumbu OX\" class=\"wp-image-1823\" width=\"356\" height=\"291\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<ul>\n<li> Garis yang sejajar dengan sumbu komputer (sumbu Y) bersifat vertikal dan selalu mengikuti ekspresi\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9c28d78386332247b427523e1e946b18_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=k.\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"48\" style=\"vertical-align: 0px;\"><\/p>\n<\/li>\n<\/ul>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/lignes-paralleles-axe-y.webp\" alt=\"garis lurus sejajar sumbu OY\" class=\"wp-image-1824\" width=\"396\" height=\"305\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-calcular-la-distancia-entre-dos-rectas-paralelas-en-el-plano\"><\/span> Cara menghitung jarak antara dua garis sejajar pada bidang datar<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> <strong>Untuk mencari jarak antara dua garis sejajar pada bidang (dalam R2), cukup ambil sebuah titik pada salah satu dari dua garis tersebut dan hitung jarak dari titik tersebut ke garis lainnya.<\/strong><\/p>\n<p> Kita dapat melakukannya dengan cara ini karena dua garis sejajar selalu berjarak sama. <\/p>\n<figure class=\"wp-block-image aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/distance-entre-un-point-et-une-ligne-en-ligne.webp\" alt=\"jarak antara dua garis sejajar\" class=\"wp-image-1960\" width=\"421\" height=\"358\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<p> Sebaliknya, jika dengan menggunakan rumus diperoleh jarak 0 satuan, berarti garis-garis tersebut saling bersentuhan di suatu titik sehingga garis-garis tersebut tidak sejajar, melainkan berpotongan, berhimpitan, atau tegak lurus. Jika mau, Anda dapat memeriksa perbedaan jenis garis ini di website kami.<\/p>\n<p> Nah, agar Anda dapat melihat caranya, kita akan menentukan jarak antara dua garis sejajar berikut sebagai contoh:<\/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-8be694174fbd8330f207d16a9fb4bb89_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r: \\ 2x-4y-6=0 \\qquad \\qquad s: \\ -x+2y+4=0\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"378\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Hal pertama yang perlu kita lakukan adalah mendapatkan titik pada salah satu garis (yang Anda inginkan). Dalam hal ini, kita akan menghitung sebuah titik pada 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-23a7daa116b8874af1538c91f8d239de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"12\" style=\"vertical-align: 0px;\"><\/p>\n<p> Untuk melakukan ini, kita harus memberi nilai pada salah satu variabel, yang akan kita lakukan misalnya<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d762821a7c6da83f02380639f43ef8fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=0:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"52\" 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-3b748efe6f89a8c847e2e6c2d5a78db8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-x+2y+4 =0 \\ \\xrightarrow{x \\ = \\ 0} \\ -0+2y+4=0\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"321\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Dan sekarang kita menghapus variabel 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-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 yang diperoleh untuk mengetahui berapa nilainya pada saat ini: <\/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-91edb06d37339167f458f910de16d57b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2y=-4\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"65\" 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-9901e9a85409e4bcbfcbffdcf97cb175_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y= \\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-50b25376eef215b49997f236615b6d6a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y= -2\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"55\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p> Oleh karena itu, titik diperoleh dari 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-ae1901659f469e6be883797bfd30f4f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> Timur:<\/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-a9176e7fde633e028a8349a5bc422e03_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(0,-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"66\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Dan setelah kita mempunyai sebuah titik pada suatu garis, kita menghitung jarak dari titik tersebut ke garis lainnya menggunakan rumus jarak dari suatu titik ke 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-8064e6650ca06c9d921e13e956ab02a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,r)= \\cfrac{\\lvert A\\cdot p_x + B\\cdot p_y +C\\rvert}{\\sqrt{A^2+B^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"232\" style=\"vertical-align: -16px;\"><\/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-4ee823834d0436c46be7a7c28faf1be3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,r)= \\cfrac{\\lvert 2\\cdot 0 + (-4)\\cdot (-2) +(-6)\\rvert}{\\sqrt{2^2+(-4)^2}}= \\cfrac{\\lvert 0+8-6\\rvert}{\\sqrt{4+16}}={\\cfrac{2}{\\sqrt{20}}=\\bm{0,45}\" title=\"Rendered by QuickLaTeX.com\" height=\"48\" width=\"503\" style=\"vertical-align: -20px;\"><\/p>\n<\/p>\n<p> <strong>Oleh karena itu, jarak antara dua garis sejajar setara dengan 0,45 satuan<\/strong> . <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-rectas-paralelas\"><\/span> Garis Paralel Memecahkan Masalah<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> Latihan 1<\/h3>\n<p> Manakah dari garis berikut yang 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-1baec7cae9d15180df86f9cf4f44d828_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{array}{l} r: \\ y=2x+3 \\\\[2ex] s: \\ y=3x-2 \\\\[2ex] q: \\ y=2x+6 \\\\[2ex] t: \\ y=-2x-4\\end{array}\" title=\"Rendered by QuickLaTeX.com\" height=\"128\" width=\"124\" 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\"> Dua garis dikatakan sejajar jika mempunyai kemiringan yang sama (dan titik potongnya berbeda). Jadi, kemiringan tiap garis 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-512039eaf89f61a38ddd4724a96d039d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m_r = 2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"55\" style=\"vertical-align: -3px;\"><\/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-b50095724cfd60e7a20c1c145394fee0_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m_s = 3\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"55\" style=\"vertical-align: -3px;\"><\/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-2be6b5987a10ce55ec47debd551d580a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m_q = 2\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"55\" style=\"vertical-align: -6px;\"><\/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-ae30bb82aed2e9e6a77ef4c906ac5c1e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m_t = -2\" title=\"Rendered by QuickLaTeX.com\" height=\"15\" width=\"67\" style=\"vertical-align: -3px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Jadi hanya garis-garisnya saja yang 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-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<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-a1b621a0854b2580a57fcbae256008ab_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"q,\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"13\" style=\"vertical-align: -4px;\"><\/p>\n<p> karena hanya mereka yang memiliki kemiringan yang sama.<\/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 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-eec55dd78ba1e0bf402e6965d873a799_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(0,2).\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"57\" 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-4697696776778fdba7b01dd73bcfe645_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r: \\; y=3x-1\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" 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 3:<\/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-0082d45adbb746641eb28f250a819459_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"m = 3\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"48\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu, persamaan garis eksplisit 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-4def7be28b405258061bd824635dc80e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=3x+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 titik potong 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-bc3d61d91e1a1ffc3ff7ac1b3340c3c5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(0,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"52\" 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-a321d111f28eb27f561524530609d166_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y= 3x+n \\ \\xrightarrow{x=0 \\ ; \\ y=2} \\ 2=3\\cdot 0 +n\" title=\"Rendered by QuickLaTeX.com\" height=\"24\" width=\"278\" 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-c2253ecacd59d789a223b2607f36301b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2=0+ n\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"74\" 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-7cd19501d52ee520c93fcbdfd6cdefca_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2= n\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"44\" 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-7ee4508eca81496f8b48fb96e2d8e4a7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{y=3x+2}\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -4px;\"><\/p>\n<\/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> 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 4<\/h3>\n<p> Berapa jarak antara dua garis sejajar 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-9ad10fd8e20d413e433851810e823172_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"r: \\ x+3y-4=0 \\qquad \\qquad s: \\ 2x+6y+6=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\"> Pertama, kita akan memverifikasi bahwa ini adalah dua garis sejajar. Untuk ini, koefisien variabel<\/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> Dan<\/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> harus proporsional satu sama lain tetapi tidak dengan ketentuan independen:<\/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-1a5385dff1a5c143885cac238927cea7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{1}{2} = \\cfrac{3}{6}\\neq \\cfrac{-4}{6} \\ \\longrightarrow \\ \\text{Paralelas}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"220\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Memang garisnya sejajar, oleh karena itu kita dapat menerapkan prosedur tersebut.<\/p>\n<p class=\"has-text-align-left\"> Sekarang kita perlu mendapatkan titik dari salah satu garis (yang Anda inginkan). Dalam hal ini, kita akan menghitung sebuah titik pada 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-23a7daa116b8874af1538c91f8d239de_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s.\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"12\" style=\"vertical-align: 0px;\"><\/p>\n<p> Untuk melakukan ini, Anda harus menetapkan nilai ke salah satu variabel, misalnya yang akan kami lakukan<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d762821a7c6da83f02380639f43ef8fd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"x=0:\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"52\" 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-cfbc09666c2be26abbecc34491f0f0a3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"2x+6y+6=0 \\ \\xrightarrow{x \\ = \\ 0} \\ 2\\cdot 0+6y+6=0\" title=\"Rendered by QuickLaTeX.com\" height=\"23\" width=\"325\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan sekarang kita menghapus variabel 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-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 yang diperoleh untuk mengetahui nilainya pada titik ini: <\/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-d2147ae4d002aba7f27fda064a5f3d15_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"6y=-6\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"65\" 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-011e4abb1bbc3ef5f362695736e2b1f7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y= \\cfrac{-6}{6}\" 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-8330e0406bdbde3e65e8142fafceeee6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y= -1\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"55\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sehingga diperoleh titik dari 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-ae1901659f469e6be883797bfd30f4f8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"s\" title=\"Rendered by QuickLaTeX.com\" height=\"8\" width=\"8\" style=\"vertical-align: 0px;\"><\/p>\n<p> Timur:<\/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-d4834bffe8509fbc113d7be09e378a7e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(0,-1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"66\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Setelah kita mengetahui suatu titik pada suatu garis, kita menghitung jarak dari titik tersebut ke garis lainnya dengan rumus: <\/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-8064e6650ca06c9d921e13e956ab02a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,r)= \\cfrac{\\lvert A\\cdot p_x + B\\cdot p_y +C\\rvert}{\\sqrt{A^2+B^2}}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"232\" style=\"vertical-align: -16px;\"><\/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-04bdc4f7bf4e33872b9a1dae673198df_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,r)= \\cfrac{\\lvert 1\\cdot 0 + 3\\cdot (-1) +(-4)\\rvert}{\\sqrt{1^2+3^2}}= \\cfrac{7}{\\sqrt{10}}=\\bm{2,21}\" title=\"Rendered by QuickLaTeX.com\" height=\"44\" width=\"371\" style=\"vertical-align: -16px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Di sini Anda akan menemukan segala sesuatu tentang garis sejajar: apa artinya, cara menentukan apakah dua garis sejajar, sifat-sifatnya, dll. Selain itu, Anda akan dapat melihat beberapa contoh dan penyelesaian latihan garis sejajar. Apa itu garis sejajar? Garis sejajar adalah garis yang tidak pernah berpotongan, artinya meskipun lintasannya diperpanjang hingga tak terhingga, garis tersebut tidak &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/pengertian-garis-sejajar-dan-contohnya\/\"> <span class=\"screen-reader-text\">Garis sejajar<\/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-231","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>Garis paralel - 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\/pengertian-garis-sejajar-dan-contohnya\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Garis paralel - Mathority\" \/>\n<meta property=\"og:description\" content=\"Di sini Anda akan menemukan segala sesuatu tentang garis sejajar: apa artinya, cara menentukan apakah dua garis sejajar, sifat-sifatnya, dll. 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Garis sejajar adalah garis yang tidak pernah berpotongan, artinya meskipun lintasannya diperpanjang hingga tak terhingga, garis tersebut tidak &hellip; Garis sejajar Selengkapnya &raquo;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/id\/pengertian-garis-sejajar-dan-contohnya\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-07-10T20:47:48+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/droites-paralleles-a-langle.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\/pengertian-garis-sejajar-dan-contohnya\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/id\/pengertian-garis-sejajar-dan-contohnya\/\"},\"author\":{\"name\":\"Tim Mathority\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38\"},\"headline\":\"Garis sejajar\",\"datePublished\":\"2023-07-10T20:47:48+00:00\",\"dateModified\":\"2023-07-10T20:47:48+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/id\/pengertian-garis-sejajar-dan-contohnya\/\"},\"wordCount\":1172,\"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\/pengertian-garis-sejajar-dan-contohnya\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/id\/pengertian-garis-sejajar-dan-contohnya\/\",\"url\":\"https:\/\/mathority.org\/id\/pengertian-garis-sejajar-dan-contohnya\/\",\"name\":\"Garis paralel - 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