{"id":302457,"date":"2021-11-01T14:07:53","date_gmt":"2021-11-01T07:07:53","guid":{"rendered":"https:\/\/quipperhome.wpcomstaging.com\/?p=302457"},"modified":"2023-02-07T15:47:43","modified_gmt":"2023-02-07T08:47:43","slug":"koordinat-cartesius","status":"publish","type":"post","link":"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/koordinat-cartesius\/","title":{"rendered":"Materi Koordinat Cartesius: Pengertian, Sistem Koordinat dan Contoh Soal"},"content":{"rendered":"\n<figure class=\"wp-block-image\"><img fetchpriority=\"high\" decoding=\"async\" width=\"800\" height=\"533\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/07\/Koordinat-Cartesius.webp\" alt=\"Materi Koordinat Cartesius: Pengertian, Sistem Koordinat dan Contoh Soal\" class=\"wp-image-302472\" srcset=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/07\/Koordinat-Cartesius.webp 800w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/07\/Koordinat-Cartesius-768x512.webp 768w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/07\/Koordinat-Cartesius-585x390.webp?crop=1 585w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/07\/Koordinat-Cartesius-263x175.webp?crop=1 263w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Tentu Quipperian pernah memanfaatkan fitur shareloc, kan? Nah, saat Quipperian menggunakan fitur tersebut, akan muncul angka-angka yang merupakan posisi titik lokasi yang dimaksud. Susunan angka-angka itu disebut sebagai titik koordinat. Biasanya, titik koordinat itu ditulis dalam bentuk koordinat Cartesius. Ingin tahu selengkapnya?<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><b>Pengertian Koordinat Cartesius<\/b><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Koordinat Cartesius adalah sistem koordinat yang memuat angka-angka tertentu di setiap bidangnya yang ditulis dalam bentuk (x,y).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Koordinat ini ditemukan oleh seorang ahli Matematika asal Prancis, yaitu Rene Descartes.&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ciri utama koordinat Cartesius adalah adanya dua garis tegak lurus yang saling berpotongan di suatu titik. Kedua garis tersebut dinamakan sebagai sumbu koordinat.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><b>Sistem Koordinat Cartesius<\/b><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Sistem koordinat Cartesius&nbsp; memuat dua buah sumbu, yaitu sumbu yang arahnya vertikal atau biasa disebut sumbu Y dan sumbu yang arahnya horizontal atau sumbu X. Perhatikan gambar berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image alignnone wp-image-302466 size-full\"><img decoding=\"async\" width=\"596\" height=\"587\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/07\/sistem-koordinat-cartesius-1.webp\" alt=\"\" class=\"wp-image-302466\"\/><figcaption class=\"wp-element-caption\">Sumber: Pustekkom Kemdikbud<\/figcaption><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Berdasarkan gambar di atas, sumbu koordinatnya diberi warna biru. Sumbu Y disebut juga koordinat dan sumbu X disebut juga absis. Selain itu, terdapat tiga kondisi garis yaitu sebagai berikut.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><b>1. Garis yang saling sejajar<\/b><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Suatu garis dikatakan sejajar jika keduanya tidak akan pernah bertemu ujung dan pangkalnya. Hal itu karena kedua garis memiliki gradien yang sama. Contoh garis sejajar adalah garis L dan N.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><b>2. Garis yang saling tegak lurus dan berpotongan<\/b><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Dua garis dikatakan tegak lurus jika keduanya saling berpotongan di suatu titik dan membentuk sudut 90o. Garis yang saling tegak lurus adalah garis K dan N serta garis K dan sumbu X. Titik perpotongan tersebut sama dengan titik koordinat Cartesius.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\"><b>3. Garis yang memotong<\/b><\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Dua garis dikatakan memotong jika keduanya berpotongan di suatu titik. Garis yang saling berpotongan adalah garis M dan L serta garis M terhadap sumbu X dan Y. Titik perpotongan tersebut sama menunjukkan titik koordinat Cartesius.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Terdapat empat daerah pada sistem koordinat ini, yaitu daerah kuadran I, II, III, dan IV. Berikut ini contohnya.&nbsp;<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" width=\"485\" height=\"328\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/07\/kuadran.webp\" alt=\"\" class=\"wp-image-302465\"\/><\/figure>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Daerah kuadran I memiliki nilai absis (x) dan ordinat (y) yang semuanya positif.<\/li>\n\n\n\n<li>Daerah kuadran II memiliki nilai absis (x) yang semuanya negatif dan ordinat (y) yang semuanya positif.<\/li>\n\n\n\n<li>Daerah kuadran III memiliki nilai absis (x) dan ordinat (y) yang semuanya negatif.<\/li>\n\n\n\n<li>Daerah kuadran IV memiliki nilai absis (x) yang semuanya positif dan ordinat (y) yang semuanya negatif.<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Adapun rumus koordinat Cartesius adalah (x,y), dengan x = nilai absis (sumbu X) dan y = nilai ordinat (sumbu Y).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Untuk lebih jelasnya, perhatikan contoh diagram Cartesius adalah sebagai berikut.<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"563\" height=\"330\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/07\/diagram-cartesius.webp\" alt=\"\" class=\"wp-image-302464\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Pada diagram di atas, terdapat dua titik koordinat yaitu titik A dan titik B.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Untuk menuliskan titik koordinatnya, kamu tentukan dahulu nilai sumbu X dan sumbu Y-nya.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Pada diagram di atas:<\/span><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><span style=\"font-weight: 400;\">titik A = (5,10) karena absisnya berada di skala 5 dan ordinatnya berada di skala 10. Itu artinya, titik A berada di daerah kuadran I; dan<\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">titik B = (15,-5) karena absisnya berada di skala 15 dan ordinatnya berada di skala -5. Itu artinya, titik B berada di daerah kuadran IV.<\/span><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Agar Quipperian semakin paham dengan materi kali ini, yuk simak contoh soal koordinat Cartesius berikut.<\/span><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><b>Contoh Soal 1<\/b><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Sebuah bangun datar dibentuk dari titik koordinat A (-1,3), titik B (1,3), titik C (-2,1), dan titik D (2,1). Tentukan luas bangun datar tersebut!<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><b>Pembahasan:<\/b><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Pertama, kamu harus menentukan posisi titik koordinat yang disebutkan pada soal.<\/span><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><span style=\"font-weight: 400;\">Titik A (-1,3) -&gt;<\/span><span style=\"font-weight: 400;\">&nbsp;titik absis = -1, titik ordinat = 3 (kuadran II)<\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">Titik B (1,3) -&gt;<\/span><span style=\"font-weight: 400;\">&nbsp;titik absis = 1, titik ordinat = 3 (kuadran I)<\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">Titik C (-2,1) -&gt;<\/span><span style=\"font-weight: 400;\">&nbsp;titik absis = -2, titik ordinat = 1 (kuadran II)<\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">Titik D (2,1) -&gt;<\/span><span style=\"font-weight: 400;\">&nbsp;titik absis = 2, titik ordinat = 1 (kuadran I)<\/span><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Berikut ini posisi titik-titik A, B, C, dan D pada diagram Cartesius.<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"393\" height=\"346\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/07\/contoh-soal-1.webp\" alt=\"\" class=\"wp-image-302463\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Jika keempat titik dihubungkan, ternyata membentuk bangun trapesium sama kaki dengan ketentuan seperti berikut.<\/span><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><span style=\"font-weight: 400;\">Tinggi bangun = 3 satuan<\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">Sisi AB = 3 satuan<\/span><\/li>\n\n\n\n<li><span style=\"font-weight: 400;\">Sisi CD = 4 satuan<\/span><\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Dengan demikian, luas trapesium ABCDnya adalah sebagai berikut.<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"224\" height=\"169\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/07\/contoh-soal-1b.webp\" alt=\"\" class=\"wp-image-302462\" srcset=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/07\/contoh-soal-1b.webp 224w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/07\/contoh-soal-1b-200x150.webp?crop=1 200w\" sizes=\"(max-width: 224px) 100vw, 224px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\"> <\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Jadi, luas bangun datar tersebut adalah 10,5 satuan luas.<\/span><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><b>Contoh Soal 2<\/b><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Galih menggambar dua buah garis, yaitu garis P dan Q. Garis P sejajar dengan sumbu X dan memotong sumbu Y di titik koordinat (0,4).&nbsp;<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Sementara itu, garis Q sejajar sumbu Y dan memotong sumbu X di titik koordinat (5,0).&nbsp;<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Tentukan titik koordinat perpotongan garis P dan Q!<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><b>Pembahasan:<\/b><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Gambarkan garis P dan Q pada diagram Cartesius seperti berikut.<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"594\" height=\"434\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/07\/contoh-soal-2.webp\" alt=\"\" class=\"wp-image-302461\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Dari diagram Kartesius di atas, terlihat bahwa garis P dan Q berpotongan di titik koordinat (5,4).<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Jadi, garis P dan Q akan berpotongan di titik koordinat (5,4).<\/span><\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><b>Contoh Soal 3<\/b><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Koordinat titik K dan L berturut-turut adalah (-3,2) dan (-6,-1). Agar terbentuk bangun segitiga sama kaki, titik M harus diletakkan pada koordinat berapa?<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><b>Pembahasan:<\/b><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Gambarkan titik tersebut pada diagram Cartesius berikut.<\/span><\/p>\n\n\n\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"603\" height=\"268\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/07\/contoh-soal-3.webp\" alt=\"\" class=\"wp-image-302460\" srcset=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/07\/contoh-soal-3.webp 603w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/07\/contoh-soal-3-600x268.webp 600w\" sizes=\"(max-width: 603px) 100vw, 603px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Agar membentuk bangun segitiga sama kaki, titik M harus diletakkan di koordinat (-2, -1).<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Jadi, titik M harus diletakkan pada koordinat (-2,-1).<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Quipperian, sekian dulu pembahasan Quipper Blog tentang Koordinat Cartesius, ya. Semoga artikel ini cukup membantu kamu untuk memahami materi yang satu ini.<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><span style=\"font-weight: 400;\">Kalau kamu masih mau belajar materi ini lebih dalam atau materi lainnya, yuk gabung bersama <\/span><a href=\"https:\/\/subscribe.quipper.com\/signup\"><b>Quipper Video<\/b><\/a><span style=\"font-weight: 400;\">! Belajar Matematika jadi seru dan menyenangkan!<\/span><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Penulis: Eka Viandari<\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tentu Quipperian pernah memanfaatkan fitur shareloc, kan? Nah, saat Quipperian menggunakan fitur tersebut, akan muncul angka-angka yang merupakan posisi titik lokasi yang dimaksud. Susunan&hellip;<\/p>\n","protected":false},"author":99400369,"featured_media":302472,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_crdt_document":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[679384865],"tags":[],"ppma_author":[679386827,679386836],"class_list":["post-302457","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matematika"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Materi Koordinat Cartesius: Pengertian, Sistem Koordinat dan Contoh Soal - Quipper Blog<\/title>\n<meta name=\"description\" content=\"Belajar materi Koordinat Cartesius lengkap meliputi pengertian, sistem koordinat dan contoh soal beserta pembahasan - 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