{"id":307238,"date":"2022-11-04T10:12:00","date_gmt":"2022-11-04T03:12:00","guid":{"rendered":"https:\/\/quipperhome.wpcomstaging.com\/?p=307238"},"modified":"2023-02-06T10:17:38","modified_gmt":"2023-02-06T03:17:38","slug":"contoh-soal-koordinat-kartesius","status":"publish","type":"post","link":"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/contoh-soal-koordinat-kartesius\/","title":{"rendered":"Contoh Soal Koordinat Kartesius Lengkap dengan Pembahasannya"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img fetchpriority=\"high\" decoding=\"async\" width=\"1280\" height=\"853\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/pexels-peter-miklos-3986613.webp\" alt=\"\" class=\"wp-image-307242\" srcset=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/pexels-peter-miklos-3986613.webp 1280w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/pexels-peter-miklos-3986613-768x512.webp 768w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/pexels-peter-miklos-3986613-1200x800.webp 1200w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/pexels-peter-miklos-3986613-1170x780.webp 1170w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/pexels-peter-miklos-3986613-585x390.webp?crop=1 585w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2022\/11\/pexels-peter-miklos-3986613-263x175.webp?crop=1 263w\" sizes=\"(max-width: 1280px) 100vw, 1280px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Hai Quipperian, tahukah kamu jika sistem koordinat merupakan pokok bahasan wajib dalam dunia Matematika. Sistem koordinat yang umumnya dipelajari adalah sistem koordinat kartesius. Pada artikel ini, kamu akan diajak untuk melihat contoh soal koordinat kartesius lengkap beserta pembahasannya. Yuk, simak selengkapnya!<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Contoh soal 1<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Farel mendapatkan undangan di acara syukuran rumah baru Deva. Di undangan tersebut tertulis bahwa rumah Deva terletak di koordinat (7,6). Jika rumah Farel berada di koordinat (-1,6), tentukan jarak yang harus ditempuh Farel untuk sampai di rumah baru Deva!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pada soal diketahui bahwa rumah baru Deva berada di koordinat (7,6), sedangkan rumah Farel berada di koordinat (-1,6). Jika dinyatakan dalam koordinat kartesius, menjadi seperti berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/8VJgjrGZsO-aATu_NlqycXS_WODKTqyt3n3-t-t0trtgiMSAa-t_SRCZ2H92uLduW_k7BhLdibwlPhwaPrBp2bmqAg7WRR6z9r_o2Rdx_ISkpuwYOOA6Y2cLl-9dY7eyVBphgyDEZ7ZD8j76rt4MbfLNiSEUZ2WHBfqbaShJJ2_5rWeSlmh2NTVaUWSmpEi778RJuMdCkQ\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Dari koordinat di atas, terlihat bahwa posisi rumah Farel dan Deva berada di sumbu-x yang sama, yaitu 6. Artinya, Farel tidak perlu melakukan perjalanan ke arah bawah (sumbu-y). Jarak yang harus ditempuh Farel untuk sampai di rumah baru Deva adalah <em>s<\/em> = 1 satuan (kuadran II) + 7 satuan (kuadran I) = 8 satuan.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Jadi, Jarak yang harus ditempuh Farel untuk sampai di rumah baru Deva adalah 8 satuan.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Contoh soal 2<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Sebuah partikel melakukan gerakan secara beraturan. Mula-mula, partikel tersebut terletak di koordinat (0,0). Lalu, partikel bergerak sejauh 8 satuan ke atas, 8 satuan ke kiri, 8 satuan ke bawah, 8 satuan ke kanan, 7 satuan ke atas, 7 satuan ke kiri, 7 satuan ke bawah, 7 satuan ke kanan, 6 satuan ke atas, 6 satuan ke kiri, 6 satuan ke bawah, 6 satuan ke kanan, dan seterusnya. Setelah bergerak selama <em>n<\/em> kali, partikel berada di koordinat A (<em>c,d<\/em>), di mana <em>c<\/em> dan <em>d<\/em> merupakan bilangan bulat. Sementara itu, <em>n<\/em> bilangan yang cukup besar. Tentukan titik A yang dimaksud!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Diketahui sebuah partikel melakukan gerakan secara beraturan. Mula-mula, partikel tersebut terletak di koordinat (0,0). Lalu, partikel bergerak sejauh 8 satuan ke atas, 8 satuan ke kiri, 8 satuan ke bawah, 8 satuan ke kanan, 7 satuan ke atas, 7 satuan ke kiri, 7 satuan ke bawah, 7 satuan ke kanan, 6 satuan ke atas, 6 satuan ke kiri, 6 satuan ke bawah, 6 satuan ke kanan, dan seterusnya. Jika gerakan partikel tersebut dinyatakan dalam koordinat kartesius, diperoleh pola seperti berikut.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pola ke-1:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/VJniZ0IA1EmyBViHvlXogbiln4Kt2u5DeRI7W-hOjPPxquMq3Z0EEshspLfRX7hm2IhipVwRsw-QnXotdZJcfQEqn5JsgCdS71niH1ljIZ6tllnPF79XnNw3xm1GZ0Th0VBVkwGHkLxAsan3I1c5zybLtQrexaS9yEU3Vfhed9MO12HQmGQ4Cod_WHU6SzTotEpDfIHHsA\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Pola ke-2:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/UWFIm5ZYgcF7n3EBMI6nTEgoofUDvhaDqIrPoAw_IEDrL4SQnGprC-v4WrDnuj3jSQnTRK5aUXhpccfbWypk98kcrx4L_Zs8s50OqFrApaqmdlMb7cmi3cSd8LjdkEm5QakmHrNHy0bhmQ_V7uvFvOjeMMhZHqHDbMc8LS2fYfnj9J8LHubdUuWv_exSkzYHpzgTRCQpzg\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Pola ke-3:<\/p>\n\n\n\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/ZrT7Ne4vXaYI5UzaT7uyUyYjqPqC4Ja2B8wus6XYlycxkJxsrbCZefFmlt05WzWsKYojHs_clN99oc3xY2ukgBHJqMr5npNGSw4jWrLf5rGgfvQEt2N5k4_PoUq2XvXGlQF-wgNUwJq8rKDgSh2w0OXovsn5Yi4NCwChBZv0Xpl1mTuLBqgBEZgB0zJmbzN6j7dG2KBS_g\" alt=\"\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Pola tersebut akan terbentuk secara terus menerus sampai partikel bergerak selama <em>n<\/em> kali. Artinya, partikel akan bergerak secara terus menerus hingga berhenti di titik A(<em>c<\/em>,<em>d<\/em>). Titik berhentinya partikel adalah titik asal, yakni (0,0). Jadi, titik A yang dimaksud adalah A(0,0).<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Contoh soal 3<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Dua buah garis, yaitu garis K dan L, saling tegak lurus. Garis K sejajar dengan sumbu-y dan melewati titik (-4,6) dan (<em>p<\/em>, <em>q<\/em>). Sementara itu, garis L sejajar dengan sumbu-x dan melewati titik (<em>r, s<\/em>). Jika <em>r<\/em> = -2<em>p<\/em> dan <em>s<\/em> = <em>r<\/em>, tentukan nilai <em>rs &#8211; p<\/em> \u2013 <em>q<\/em> !<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Diketahui dua buah garis, yaitu garis K dan L, saling tegak lurus. Garis K sejajar dengan sumbu-y dan melewati titik (-4,6) dan (<em>p<\/em>, <em>q<\/em>). Sementara itu, garis L sejajar dengan sumbu-x dan melewati titik (<em>r,s<\/em>). Garis yang sejajar dengan sumbu-y pasti memiliki nilai absis yang sama. Artinya, <em>p<\/em> = -4.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ingat bahwa <em>r<\/em> = -2<em>p<\/em>, sehingga:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><em>r<\/em> = -2<em>p<\/em><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;&nbsp;= -2 (-4)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">&nbsp;= 8<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Mengingat <em>s<\/em> = <em>r<\/em>, maka <em>s<\/em> = 8. Artinya, koordinat titik ketiga adalah (8, 8).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Garis L sejajar dengan sumbu-x dan melalui titik (8, 8). Artinya, garis L tidak melalui titik (-4, 6), namun melalui titik (<em>p<\/em>, <em>q<\/em>). Dengan demikian, nilai <em>q<\/em> = 8.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Oleh karena <em>p<\/em> = -4, <em>q<\/em> = 8, <em>r<\/em> = 8, dan <em>s<\/em> = 8, maka:<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img decoding=\"async\" src=\"https:\/\/lh6.googleusercontent.com\/QrXEJBpVl0bfxFsywwhz6bdJcfaaAf9zTLKWYqp8Q6eTiaDsF6fGo2_1iJ-kykRo2nVxmJ4OuVwwKO27l8_4x6BvESK9EYS2oGf_HGxM3LkyXO1r_eqrFVtRhenW34WqHJnSMuk97ZfrMkkDmWhkyFtR4TMVBp2PAN02DjA0VeHzfzAxM4odspiMDuAV6TZ7bPEFy6WZTQ\" alt=\"\" width=\"257\" height=\"97\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Jadi, nilai <em>rs &#8211; p<\/em> \u2013 <em>q <\/em>= 60.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Contoh soal 4<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Bu Jumi memiliki sebidang tanah berbentuk persegipanjang. Rencananya, tanah tersebut akan digunakan sebagai tempat penyemaian benih cabe. Jika digambarkan secara sederhana pada koordinat kartesius, titik koordinat tanah Bu Jumi adalah P(2, 9), Q(10, 9), dan R(2, 3). Tentukan luas tanah Bu Jumi yang akan digunakan sebagai tempat persemaian benih cabe!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Diketahui:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Bu Jumi memiliki sebidang tanah berbentuk persegipanjang. Titik koordinat tanahnya adalah P(2, 9), Q(10, 9), dan R(2, 3).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ditanya: <em>L<\/em> =?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Mula-mula, kamu harus mencari titik koordinat S dengan menggambarkan tanah Bu Jumi dalam koordinat kartesius seperti berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/VAp3EnVq90GV7T9IgYrPyPaDPPjt-HvY5f4aReLl6sHjkSDR3MQxP1ticXIMN3nrt2mtPFvREYpxsJAvmCK8c3u85GTkwo-k58wLGWpN5iRNjLNfaMepLPXgFVdnXGr5EwhljXJYFUnsVkwp2hzNnBHF4JzL5rvmN0y9eQbDAjuR8LYtitaWGWRqpPEJAoQLt6hGrnUidg\" alt=\"\" width=\"315\" height=\"281\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Dari penggambaran di atas, koordinat titik Snya adalah (10, 3). Dengan demikian, luas tanah Bu Jumi dinyatakan sebagai berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh3.googleusercontent.com\/pbtsql6dX58cp6tOjtJcs_h-gryjKZ_5f_iZ-JmgAXybYdulnFWJdZiM1b_YgWBCslgiBaWVfMhsG-dUQBoCloI7ZwCDpQsIuqPT_h03F3U1kkO-ozg4KEy1MRox1FaZn6YVXErout7z_UmHHzvHZn71iFoF8uxtpNSBQT3rcMgj_nATDbJctimExBr2EbYK8fq7FYnVXQ\" alt=\"\" width=\"151\" height=\"110\"\/><\/figure>\n\n\n\n<h2 class=\"wp-block-heading\"><strong>Contoh soal 5<\/strong><\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Seorang atlet sedang mengikuti lomba lari di lintasan yang berbentuk segienam. Titik pusat lintasan itu berada di koordinat (0, 0). Salah satu titik pojok lintasan atlet berlari berjarak 3<em>a<\/em> dari titik pusatnya. Jika atlet tersebut berlari sebanyak <em>n<\/em> kali, tentukan panjangnya lintasan yang dilalui si atlet!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Diketahui bahwa seorang atlet sedang mengikuti lomba lari di lintasan yang berbentuk segienam. Titik pusat lintasan itu berada di koordinat (0, 0). Salah satu titik pojok lintasan atlet berlari berjarak 3<em>a<\/em> dari titik pusatnya. Jika digambarkan, posisi lintasan lari atlet tersebut adalah seperti berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh5.googleusercontent.com\/HRM-6D4b7SXJu9cW-7eOdqaatkEpGSkttWcvSWiyYIccRJgqYyf9YWRp_HaEybciJZqXYVHmjNuHUWAI5V7LqpidF1u0H1YqEN8D8zWCPyRFCzqsTfhZUj0vV7URPUU6nsRf3Be8kTUQP6cIGGAK3Uvy_urlnr_tJuIaC5vagcifqUXaJhBcMa4uQJ5PqVPdKUVIt56Dkw\" alt=\"\" width=\"267\" height=\"196\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Titik koordinat salah satu titik pojok segienam adalah (3<em>a<\/em>, 0). Oleh karena segienamnya beraturan, maka panjang semua sisi segienamnya sama, yaitu 3<em>a<\/em>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Untuk mencari panjang lintasan yang ditempuh atlet setelah berlari <em>n<\/em> kali, kamu harus tahu dahulu keliling segienamnya.<\/p>\n\n\n\n<figure class=\"wp-block-image is-resized\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/lh4.googleusercontent.com\/hq1apNsY-g4T45xCVn5531_SKqRvSatk-TmzV_Ybo_6FzzLiKZ9vVVqs0ugjhv3vJCMS0Fv-nZAewaq2sSp9YFCmBnGT1HChTpJGHYAQnP6xUCZBSGLCr094k17sI-ZyU9Uk2_Kd8e4kQMQpFioRVMaMvDxHICBTaVYOJP1loa2V_LxXc1n9JMqKkGSgo4Zs7q3jKhzzlQ\" alt=\"\" width=\"96\" height=\"93\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Jika atlet berlari sebanyak <em>n<\/em> kali, maka panjang lintasannya adalah <sub><\/sub>&nbsp;<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Jadi, panjang lintasan yang dilalui oleh atlet adalah 18<em>an<\/em>.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Itulah pembahasan Quipper Blog kali ini. Semoga bermanfaat, ya. Jika kamu ingin melihat video lengkapnya tentang sistem koordinat kartesius, yuk buruan gabung <a href=\"https:\/\/quipper.com\/id\/video\/\">Quipper Video.<\/a> Salam Quipper!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Hai Quipperian, tahukah kamu jika sistem koordinat merupakan pokok bahasan wajib dalam dunia Matematika. Sistem koordinat yang umumnya dipelajari adalah sistem koordinat kartesius. Pada&hellip;<\/p>\n","protected":false},"author":156447303,"featured_media":307242,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_post_was_ever_published":false},"categories":[679384888,679384865],"tags":[679386714],"ppma_author":[679386823,679386836],"class_list":["post-307238","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mapel","category-matematika","tag-matematika-kelas-8"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.8 - 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