{"id":73,"date":"2023-09-16T13:02:19","date_gmt":"2023-09-16T13:02:19","guid":{"rendered":"https:\/\/mathority.org\/id\/contoh-poin-selaras-latihan-yang-diselesaikan\/"},"modified":"2023-09-16T13:02:19","modified_gmt":"2023-09-16T13:02:19","slug":"contoh-poin-selaras-latihan-yang-diselesaikan","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/contoh-poin-selaras-latihan-yang-diselesaikan\/","title":{"rendered":"Poin-poin yang selaras"},"content":{"rendered":"<p>Di halaman ini Anda akan menemukan penjelasan tentang apa itu titik sejajar. Anda juga akan melihat semua metode yang tersedia untuk menentukan apakah 3 (atau lebih) titik sejajar. Terlebih lagi, Anda akan menemukan beberapa contoh dan bahkan latihan yang diselesaikan sehingga Anda dapat berlatih. <\/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%bfque-significa-que-los-puntos-estan-alineados\"><\/span> Apa maksudnya titik-titik tersebut sejajar?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Dalam geometri analitik, <strong>tiga titik atau lebih disejajarkan<\/strong> jika semuanya berada pada garis yang sama, yaitu jika titik-titik tersebut dapat dihubungkan dengan menggambar garis lurus di antara titik-titik tersebut. <\/p>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-105\"><\/div>\n<\/div>\n<p> Jelasnya, 2 titik akan selalu sejajar, karena Anda selalu dapat menarik garis di antara dua titik. Namun, tiga titik tidak harus berada pada garis yang sama. Pada dasarnya, ada dua metode untuk mengetahui apakah 3 titik atau lebih sejajar:<\/p>\n<ul>\n<li> <strong>Metode vektor<\/strong> : terdiri dari melihat apakah vektor-vektor yang membentuk titik-titik sebanding.<\/li>\n<li> <strong>Metode persamaan garis<\/strong> : terdiri dari menentukan apakah titik-titik tersebut termasuk dalam garis yang sama.<\/li>\n<\/ul>\n<p> Di bawah ini adalah penjelasan setiap prosedur dan contohnya sehingga Anda dapat memutuskan mana yang terbaik untuk Anda. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-saber-si-3-o-mas-puntos-estan-alineados-con-el-metodo-de-los-vectores\"><\/span> Bagaimana cara mengetahui apakah 3 (atau lebih) titik sejajar dengan metode vektor <span class=\"ez-toc-section-end\"><\/span><\/h2>\n<div style=\"background-color:#FFCC8080;padding-top: 20px; padding-bottom: 0.5px; padding-right: 30px; padding-left: 30px; border: 2px solid #FFB74D; border-radius:20px;\">\n<p style=\"text-align:left\"> Mempertimbangkan tiga poin:<\/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-88818892831a9ada6aa3f369b1406d03_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(x_1,y_1) \\quad B(x_2,y_2) \\quad C(x_3,y_3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"244\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\"> Ketiga titik tersebut sejajar jika vektornya<\/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-243865b783ec40e03ec861ac2ebcb279_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AB}\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"27\" 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-f10db290eb97b835b1c57091b3a33992_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{BC}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"28\" style=\"vertical-align: 0px;\"><\/p>\n<p> mempunyai arah yang sama, artinya komponen-komponennya sebanding. <\/p>\n<\/div>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-106\"><\/div>\n<\/div>\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\/points-alignes-1.webp\" alt=\"titik-titik yang sejajar pada suatu bidang\" class=\"wp-image-1121\" width=\"267\" height=\"267\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Mari kita lihat contoh bagaimana hal ini dilakukan:<\/p>\n<ul>\n<li> Tentukan apakah 3 poin berikut sejajar:<\/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-150343d1934b000b9bd8188f1418eb3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(1,2) \\quad B(4,4) \\quad C(-2,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"208\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Pertama, kita menghitung vektor antar titik. Cukup menghitung dua vektor 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-987e7356216c577b32947f23519c407f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AB} = B - A = (4,4)- (1,2) = (3,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"287\" 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-ee1e4b4246ed129cc3f7adcb5315edc7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{BC} = C-B =(-2,0)- (4,4)= (-6,-4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"330\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Dan kemudian kita periksa apakah koordinat vektornya 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-16253047910ee22fb08aebcdc967278f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{-6}{3} = \\cfrac{-4}{2} = -2\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"132\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Dengan membagi komponen X dan komponen Y dari kedua vektor tersebut diperoleh hasil yang sama (-2), sehingga vektor-vektor tersebut mempunyai arah yang sama dan oleh karena itu <strong>titik-titiknya sejajar<\/strong> .<\/p>\n<p> Cara ini juga dapat digunakan untuk mengetahui apakah tiga titik atau lebih sejajar dalam ruang (pada R3), yang perlu ditambah hanyalah memeriksa apakah komponen ketiga dari kedua vektor tersebut (komponen Z) juga proporsional.<\/p>\n<p> Jika artikel ini bermanfaat bagi Anda, Anda mungkin juga tertarik untuk mengetahui cara menghitung <a href=\"https:\/\/mathority.org\/id\/rumus-titik-tengah-vektor-segmen\/\">titik tengah antara dua titik<\/a> , karena tentunya mencari titik tengah 2 titik adalah cara menentukan titik ketiga yang sejajar dengan dua titik lainnya. Anda dapat melihat cara melakukannya di halaman tertaut, selain itu Anda juga dapat melihat contoh dan latihan yang diselesaikan langkah demi langkah. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"como-averiguar-si-3-o-mas-puntos-estan-alineados-con-el-metodo-de-la-ecuacion-de-la-recta\"><\/span> Cara mengetahui 3 titik (atau lebih) sejajar dengan metode persamaan garis lurus <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> Seperti yang baru saja kita lihat di bagian sebelumnya, salah satu cara mempelajari keselarasan 3 titik atau lebih adalah dengan menggunakan vektor-vektor yang dapat terbentuk di antara titik-titik tersebut. Nah, cara lainnya adalah memulai dengan persamaan garis: <\/p>\n<div style=\"background-color:#FFCC8080;padding-top: 20px; padding-bottom: 0.5px; padding-right: 30px; padding-left: 30px; border: 2px solid #FFB74D; border-radius:20px;\">\n<p style=\"text-align:left\"> Mempertimbangkan tiga poin:<\/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-88818892831a9ada6aa3f369b1406d03_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(x_1,y_1) \\quad B(x_2,y_2) \\quad C(x_3,y_3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"244\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\"> Ketiga titik tersebut sejajar jika semuanya berada pada garis yang sama. Oleh karena itu, untuk mengetahui apakah tiga titik atau lebih sejajar, langkah-langkah berikut harus diikuti:<\/p>\n<ol style=\"color:#42A5F5\">\n<li> <span style=\"color:#0c0c0c\">Tentukan persamaan garis yang melalui dua dari tiga titik.<\/span><\/li>\n<li> <span style=\"color:#0c0c0c\">Periksa apakah titik ketiga juga termasuk dalam garis tersebut. Dalam hal ini berarti 3 titik tersebut sejajar, namun jika syarat tersebut tidak terpenuhi berarti titik-titik tersebut tidak sejajar.<\/span> <\/li>\n<\/ol>\n<\/div>\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\/formule-de-3-points-alignes.webp\" alt=\"rumus tiga titik sejajar\" class=\"wp-image-1143\" width=\"275\" height=\"262\" srcset=\"\" sizes=\"auto, \" data-src=\"\"><\/figure>\n<\/div>\n<p> Sebagai contoh, kita akan menyelesaikan latihan menggunakan metode ini:<\/p>\n<ul>\n<li> Periksa apakah 3 poin berikut selaras:<\/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-0955033d07a0ffa4311b6477fec3b153_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(3,1) \\quad B(1,4) \\quad C(5,-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"208\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Pertama-tama kita harus menghitung persamaan garis yang melalui titik A dan B. Oleh karena itu, kita mencari vektor arah 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-4a80df873f9ac7ae3d132a551e8de7e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AB} = B-A = (1,4) - (3,1) = (-2,3)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"301\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Sekarang Anda harus membuat persamaan garis, Anda dapat memilih jenis yang Anda inginkan: parametrik, implisit, umum, dll. Namun dalam hal ini kita akan menggunakan persamaan kontinu. Jadi persamaan garis kontinu yang melalui titik A dan titik B 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-b6f94bd712f1b5eb3e086f90b1ab497a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x-3}{-2}=\\cfrac{y-1}{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"106\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p> Setelah kita mendapatkan persamaan garisnya, kita harus memeriksa apakah titik lainnya juga termasuk dalam garis yang sama. Caranya, kita substitusikan koordinat titik C 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-45717c1e198eb634f35329c7af91f1c2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{5-3}{-2}=\\cfrac{-2-1}{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"127\" 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-fb2241c675eff5beda831f375678af8f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{2}{-2}=\\cfrac{-3}{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"79\" 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-962c6302723831d83dd3adb9955b8ee8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-1=-1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"67\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Kita mendapat hasil seri, jadi titiknya memenuhi persamaan garis. Oleh karena itu, <strong>ketiga titik tersebut segaris<\/strong> .<\/p>\n<p> Perlu diperhatikan bahwa himpunan titik-titik yang sejajar tidak harus berjarak sama, artinya jarak antara beberapa titik yang sejajar bisa saja berbeda. Perbedaan kedua konsep tersebut dapat Anda lihat pada penjelasan <a href=\"https:\/\/mathority.org\/id\/rumus-jarak-antara-dua-titik-contoh-geometri-dan-latihan-soal-yang-diselesaikan\/\">jarak antara dua titik (geometri)<\/a> , di mana Anda juga dapat melihat contoh dan latihan yang diselesaikan langkah demi langkah. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-puntos-alineados\"><\/span> Menyelesaikan latihan titik-titik sejajar<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> Latihan 1<\/h3>\n<p> Tentukan apakah 3 poin 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-508fe1a58d29e8dd0e5f25e9c431e07e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(1,1) \\quad B(2,-1) \\quad C(-2,7)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"222\" style=\"vertical-align: -5px;\"><\/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 solusinya<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Kita dapat memilih salah satu dari dua metode yang telah kita lihat untuk memecahkan masalah tersebut. Dalam hal ini kita akan menggunakan metode vektor.<\/p>\n<p class=\"has-text-align-left\"> Pertama, kita menghitung vektor antar 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-8a4c888c595453f36f08fd6efb79c879_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AB} = B - A = (2,-1)- (1,1) = (1,-2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"315\" 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-2ee5603a2cc587ab3dcffa296aeef0e2_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{BC} = C-B =(-2,7)- (2,-1)= (-4,8)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"330\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan sekarang kita periksa apakah koordinat Cartesian dari vektor-vektor tersebut 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-e78dec44294d4d784e5cf93ff4cf6fd4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{-4}{1} = \\cfrac{8}{-2} = -4\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"125\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dengan membagi komponen X dan komponen Y kedua vektor satu sama lain diperoleh hasil yang sama (-4), sehingga arah vektor-vektor tersebut sama. Fakta yang menunjukkan bahwa <strong>titik-titik 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> Diberikan 3 poin:<\/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-a211b45658e3ecc9a6d99ab9c25cef6f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(6,3) \\quad B(4,-3) \\quad C(4,5)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"208\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Tentukan mana yang sejajar dengan dua titik 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-e69edcc5f0f57a26e5113fc037b79a33_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"D(3,-1) \\quad E(2,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"139\" style=\"vertical-align: -5px;\"><\/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 solusinya<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Dalam hal ini kita akan menggunakan metode persamaan garis lurus, sehingga kita akan menyimpan beberapa perhitungan.<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu kita menghitung persamaan kontinu garis yang melalui titik D dan E: <\/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-b49904508e43c2689dbd43b72c54a343_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{DE} = E-D = (2,1) - (3,-1) = (-1,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"318\" 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-e2006fb32975727fc10dea3e135fcc1a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{x-3}{-1}=\\cfrac{y+1}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"106\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan sekarang mari kita periksa titik mana yang sesuai dengan persamaan garis, sehingga sejajar dengan titik D dan E, dan mana yang tidak.<\/p>\n<p class=\"has-text-align-left\"> Kami memeriksa titik A: <\/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-1719d4a555050da2ea17f56d610e569e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{6-3}{-1}=\\cfrac{3+1}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"105\" 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-c9c8e342285cc2960cd1ac221202c854_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{3}{-1}=\\cfrac{4}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"57\" 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-661377ab0472015b8558320f2c01ef58_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-3\\neq 2\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"53\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Persamaan garis tersebut tidak benar sehingga <strong>titik A tidak sejajar dengan titik D dan E.<\/strong><\/p>\n<p class=\"has-text-align-left\"> Kami sekarang memeriksa poin B: <\/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-c627d26517f60ddc4ac6921f8e8f3e07_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{4-3}{-1}=\\cfrac{-3+1}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"127\" 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-edc9b8b5c0349b7f757d00cbe0dc7d02_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{1}{-1}=\\cfrac{-2}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"79\" 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-9f4f670113c39f3a05ad405e92176773_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-1= -1\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"67\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dalam hal ini persamaan garis terpenuhi, sehingga <strong>titik B segaris dengan titik D dan E.<\/strong><\/p>\n<p class=\"has-text-align-left\"> Dan terakhir kita ulangi prosesnya dengan poin C: <\/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-fca526dda7c61b4d49f377dfb3bddc3a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{4-3}{-1}=\\cfrac{5+1}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"39\" width=\"105\" 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-50dc4b51810a1541b1c647128826857f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{1}{-1}=\\cfrac{6}{2}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"57\" 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-0967dbdc2483e19c1585ce93af3f75b5_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-1\\neq 3\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"54\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Persamaan garis tersebut tidak benar sehingga <strong>titik C tidak sejajar dengan titik D dan E.<\/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> Menemukan nilai dari 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-3422b6bb5c160593658b7c39425d9880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> sehingga 3 poin berikut selaras: <\/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-3d24a8001da7ee9bc585c9cde8c495ba_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(k,5) \\quad B(-1,-4) \\quad C(k-1,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"254\" style=\"vertical-align: -5px;\"><\/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 solusinya<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Dalam hal ini kita akan menggunakan metode vektor.<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu kami mencoba menghitung vektor antara titik-titik 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-b81dc7bc509c6e2589c62f78934129ff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{AB} = B - A = (-1,-4)- (k,5) = (-1-k,-9)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"375\" 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-e4c6260bf90e1ffb02aaf6dc7297cda1_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\vv{BC} = C-B =(k-1,2)- (-1,-4)= (k,6)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"348\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Agar kolinearitas tiga titik terpenuhi, koordinat kedua vektor harus proporsional. Oleh karena itu kami menerapkan ketentuan 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-8478d3909be370139f11503805517fcd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\cfrac{-1-k}{k} = \\cfrac{-9}{6}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"119\" style=\"vertical-align: -12px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan kami memecahkan persamaan: <\/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-476a5e44e3e0eb3057a5cc26e27cb77b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"(-1-k)\\cdot 6 = -9 \\cdot k\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"157\" 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-a2a9cb146b7bb7de4a735e0c2a409207_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-6-6k = -9k\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"118\" 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-9dedb7656b3248213103847e15e46388_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"-6k+9k = 6\" title=\"Rendered by QuickLaTeX.com\" height=\"14\" width=\"104\" 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-3eba160999a1f5f128b874b5d8d18a60_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"3k = 6\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"51\" 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-01f0a6048dc5d48632c2e10fa8179c47_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k=\\cfrac{6}{3}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"44\" 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-20b989bf2c21866deb6a2b220f87dfff_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{k=2}\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"41\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sehingga 3 titik 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-3422b6bb5c160593658b7c39425d9880_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"k\" title=\"Rendered by QuickLaTeX.com\" height=\"12\" width=\"9\" style=\"vertical-align: 0px;\"><\/p>\n<p> harus bernilai 2.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Di halaman ini Anda akan menemukan penjelasan tentang apa itu titik sejajar. Anda juga akan melihat semua metode yang tersedia untuk menentukan apakah 3 (atau lebih) titik sejajar. Terlebih lagi, Anda akan menemukan beberapa contoh dan bahkan latihan yang diselesaikan sehingga Anda dapat berlatih. Apa maksudnya titik-titik tersebut sejajar? Dalam geometri analitik, tiga titik atau &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/contoh-poin-selaras-latihan-yang-diselesaikan\/\"> <span class=\"screen-reader-text\">Poin-poin yang selaras<\/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-73","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>\u25b7 Bagaimana saya tahu jika 3 (atau lebih) titik sejajar? \u2705<\/title>\n<meta name=\"description\" content=\"Apa artinya jika tiga titik sejajar? \u2705 Penjelasan cara menentukan apakah 3 (atau lebih) titik sejajar. \u2705 Contoh dan latihan yang diselesaikan. \u2705\" \/>\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-poin-selaras-latihan-yang-diselesaikan\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u25b7 Bagaimana saya tahu jika 3 (atau lebih) titik sejajar? \u2705\" \/>\n<meta property=\"og:description\" content=\"Apa artinya jika tiga titik sejajar? \u2705 Penjelasan cara menentukan apakah 3 (atau lebih) titik sejajar. \u2705 Contoh dan latihan yang diselesaikan. \u2705\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathority.org\/id\/contoh-poin-selaras-latihan-yang-diselesaikan\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-09-16T13:02:19+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-88818892831a9ada6aa3f369b1406d03_l3.png\" \/>\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=\"4 menit\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathority.org\/id\/contoh-poin-selaras-latihan-yang-diselesaikan\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathority.org\/id\/contoh-poin-selaras-latihan-yang-diselesaikan\/\"},\"author\":{\"name\":\"Tim Mathority\",\"@id\":\"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38\"},\"headline\":\"Poin-poin yang selaras\",\"datePublished\":\"2023-09-16T13:02:19+00:00\",\"dateModified\":\"2023-09-16T13:02:19+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathority.org\/id\/contoh-poin-selaras-latihan-yang-diselesaikan\/\"},\"wordCount\":886,\"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-poin-selaras-latihan-yang-diselesaikan\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathority.org\/id\/contoh-poin-selaras-latihan-yang-diselesaikan\/\",\"url\":\"https:\/\/mathority.org\/id\/contoh-poin-selaras-latihan-yang-diselesaikan\/\",\"name\":\"\u25b7 Bagaimana saya tahu jika 3 (atau lebih) titik sejajar? 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