{"id":313276,"date":"2023-02-16T13:23:33","date_gmt":"2023-02-16T06:23:33","guid":{"rendered":"https:\/\/quipperhome.wpcomstaging.com\/?p=313276"},"modified":"2023-02-16T13:24:58","modified_gmt":"2023-02-16T06:24:58","slug":"dilatasi-matematika","status":"publish","type":"post","link":"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/dilatasi-matematika\/","title":{"rendered":"Rumus dan Jenis-Jenis Dilatasi Matematika serta Contoh Soal"},"content":{"rendered":"\n<figure class=\"wp-block-image size-full\"><img fetchpriority=\"high\" decoding=\"async\" width=\"1280\" height=\"780\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/02\/Rumus-dan-Jenis-Jenis-Dilatasi-Matematika-serta-Contoh-Soal.webp\" alt=\"Rumus dan Jenis-Jenis Dilatasi Matematika serta Contoh Soal\" class=\"wp-image-313328\" srcset=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/02\/Rumus-dan-Jenis-Jenis-Dilatasi-Matematika-serta-Contoh-Soal.webp 1280w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/02\/Rumus-dan-Jenis-Jenis-Dilatasi-Matematika-serta-Contoh-Soal-768x468.webp 768w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/02\/Rumus-dan-Jenis-Jenis-Dilatasi-Matematika-serta-Contoh-Soal-1200x731.webp 1200w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/02\/Rumus-dan-Jenis-Jenis-Dilatasi-Matematika-serta-Contoh-Soal-1170x713.webp 1170w\" sizes=\"(max-width: 1280px) 100vw, 1280px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Hai Quipperian, bagaimana kabarnya? Semoga selalu sehat, ya.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pernahkah kamu memanfaatkan tools zoom\/perbesaran saat sedang memfoto suatu objek? Jika kamu memperbesar suatu objek melalui kamera, pasti akan muncul keterangan 1,5x; 2x; 3,5x; 3,9x; dan seterusnya kan? Di dalam Matematika, keterangan 2x atau 4x itu merupakan faktor pengali sementara proses perbesaran yang kamu lakukan disebut dilatasi. Lalu, apa yang dimaksud dilatasi itu? Daripada penasaran, yuk simak selengkapnya!<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Pengertian Dilatasi<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Dilatasi adalah perubahan titik suatu objek pada bidang geometri berdasarkan nilai faktor pengalinya. Pada transformasi jenis ini, ukuran bayangan bisa berbeda dengan ukuran bendanya. Namun, bisa juga ukuran bayangannya tetap. Namun, bentuknya tetap sama, ya. Mengapa demikian? Hal itu karena adanya faktor pengali. Misalnya suatu objek diperbesar dengan faktor pengali = 2, maka bayangan objek tersebut memiliki ukuran dua kali ukuran objek mula-mula dan jarak bayangan terhadap titik pusatnya juga dua kali lebih jauh dari jarak objek dan titik pusat mula-mula.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Faktor Pengali Pada Dilatasi<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Faktor pengali merupakan faktor penentu letak dan ukuran suatu objek hasil dilatasi. Lalu, seperti apa hubungan antara dilatasi dan faktor pengali?<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Faktor pengali lebih besar dari satu (k > 1) akan mengakibatkan pembesaran ukuran objek dan searah dengan sudut dilatasi objek awalnya.<\/li>\n\n\n\n<li>Faktor pengali sama dengan satu (k = 1) tidak mengakibatkan perubahan ukuran atau posisi objek.<\/li>\n\n\n\n<li>Faktor pengali antara 0 dan 1 (0 &lt; k &lt; 1) mengakibatkan pengecilan ukuran objek dan searah dengan sudut dilatasi awalnya.<\/li>\n\n\n\n<li>Faktor pengali antara -1 dan 0 (-1 &lt; k &lt; 0) mengakibatkan pengecilan ukuran objek dan memiliki arah yang berlawanan dengan sudut dilatasi awalnya.<\/li>\n\n\n\n<li>Faktor pengali sama dengan -1 (k = -1) tidak mengakibatkan perubahan ukuran objek, namun arahnya berlawanan dengan sudut dilatasi awalnya.<\/li>\n\n\n\n<li>Faktor pengali lebih kecil dari -1 (k &lt; &#8211; 1) mengakibatkan pembesaran ukuran objek dan memiliki arah berlawanan dengan sudut dilatasi awalnya.<\/li>\n<\/ul>\n\n\n\n<div class=\"baca\">\n<p><span class=\"head_baca\">Baca Juga: <\/span> <a href=\"https:\/\/www.quipper.com\/id\/blog\/mapel\/matematika\/transformasi-geometri\/\">Materi Transformasi Geometri Rumus, Jenis: Translasi, Refleksi, Rotasi &#038; Dilatasi<\/a><\/p>\n<\/div>\n\n\n\n<h2 class=\"wp-block-heading\">Jenis-Jenis Dilatasi<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Berdasarkan titik pusatnya, dilatasi dibagi menjadi dua, yaitu dilatasi terhadap titik pusat (0, 0) dan dilatasi terhadap titik pusat (a, b). Apa perbedaan antara keduanya?<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Dilatasi Terhadap Titik Pusat (0, 0)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Bentuk umum dilatasi titik A terhadap titik pusat (0, 0) bisa dinyatakan sebagai berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"174\" height=\"23\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/02\/Bentuk-umum-dilatasi-titik-A-terhadap-titik-pusat.webp\" alt=\"\" class=\"wp-image-313281\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Bentuk penulisan di atas menunjukkan bahwa titik A yang berkoordinat (x, y) mengalami dilatasi terhadap titik pusat (0, 0) dengan faktor pengali k, sehingga menghasilkan titik A\u2019 yang berkoordinat (x\u2019, y\u2019).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Nah, koordinat (x\u2019, y\u2019), kamu bisa tentukan menggunakan persamaan matriks seperti di bawah ini.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" width=\"204\" height=\"78\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/02\/koordinat-x-y-kamu-bisa-tentukan-menggunakan-persamaan-matriks-seperti-di-bawah-ini.webp\" alt=\"\" class=\"wp-image-313283\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Agar semakin paham, simak contoh soalnya ya.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Suatu objek berbentuk persegipanjang PQRS berada di bidang koordinat Cartesius seperti berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"574\" height=\"533\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/02\/Suatu-objek-berbentuk-persegipanjang-PQRS-berada-di-bidang-koordinat-Cartesius-seperti-berikut.webp\" alt=\"Suatu objek berbentuk persegipanjang PQRS berada di bidang koordinat Cartesius seperti berikut\" class=\"wp-image-313285\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Jika objek tersebut didilatasikan terhadap titik pusat dengan k = 2, tentukan bentuk bayangan yang terjadi!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Mula-mula, tentukan dahulu koordinat titik P, titik Q, titik R, dan titik S seperti pada tabel.<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th>Titik<\/th><th>Koordinat<\/th><\/tr><\/thead><tbody><tr><td>P<\/td><td>(1, 3)<\/td><\/tr><tr><td>Q<\/td><td>(4, 3)<\/td><\/tr><tr><td>R<\/td><td>(1, 2)<\/td><\/tr><tr><td>S<\/td><td>(4, 2)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Selanjutnya, tentukan koordinat titik P\u2019, titik Q\u2019, titik R\u2019, dan titik S\u2019 dengan persamaan dilatasi terhadap titik pusat.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Titik P\u2019<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"214\" height=\"247\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/02\/Titik-P.webp\" alt=\"\" class=\"wp-image-313288\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Dengan demikian P\u2019 = (2, 6)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Titik Q\u2019<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"205\" height=\"243\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/02\/Titik-Q.webp\" alt=\"\" class=\"wp-image-313290\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Dengan demikian Q\u2019 = (8, 6)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Titik R\u2019<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"214\" height=\"241\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/02\/Titik-R.webp\" alt=\"\" class=\"wp-image-313292\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Dengan demikian R\u2019 = (2, 4)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Titik S\u2019<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"216\" height=\"240\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/02\/Titik-S.png\" alt=\"\" class=\"wp-image-313293\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Dengan demikian S\u2019 = (8, 4)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Diperoleh:<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table><thead><tr><th>Titik awal<\/th><th>Koordinat<\/th><th>Titik akhir<\/th><th>Koordinat<\/th><\/tr><\/thead><tbody><tr><td>P<\/td><td>(1, 3)<\/td><td>P\u2019<\/td><td>(2, 6)<\/td><\/tr><tr><td>Q<\/td><td>(4, 3)<\/td><td>Q\u2019<\/td><td>(8, 6)<\/td><\/tr><tr><td>R<\/td><td>(1, 2)<\/td><td>R\u2019<\/td><td>(2, 4)<\/td><\/tr><tr><td>S<\/td><td>(4, 2)<\/td><td>S\u2019<\/td><td>(8, 4)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Jika digambarkan dalam koordinat Cartesius menjadi:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"607\" height=\"453\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/02\/Jika-digambarkan-dalam-koordinat-Cartesius-menjadi.webp\" alt=\"\" class=\"wp-image-313296\" srcset=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/02\/Jika-digambarkan-dalam-koordinat-Cartesius-menjadi.webp 607w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/02\/Jika-digambarkan-dalam-koordinat-Cartesius-menjadi-400x300.webp?crop=1 400w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/02\/Jika-digambarkan-dalam-koordinat-Cartesius-menjadi-200x150.webp?crop=1 200w\" sizes=\"(max-width: 607px) 100vw, 607px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Terlihat kan jika gambar objeknya mengalami pembesaran dengan arah yang sama dengan sudut dilatasi awalnya? Sampai sini, apakah Quipperian sudah paham? Jika sudah, yuk lanjut ke pembahasan selanjutnya.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Dilatasi Terhadap Titik Pusat (a, b)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Jika titik A mengalami dilatasi terhadap titik pusat (a, b) dengan faktor pengali k, maka secara matematis bisa dinyatakan sebagai:<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"302\" height=\"60\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/02\/Dilatasi-Terhadap-Titik-Pusat-a-b.webp\" alt=\"\" class=\"wp-image-313298\" srcset=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/02\/Dilatasi-Terhadap-Titik-Pusat-a-b.webp 302w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/02\/Dilatasi-Terhadap-Titik-Pusat-a-b-300x60.webp 300w\" sizes=\"(max-width: 302px) 100vw, 302px\" \/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Lalu, bagaimana cara menentukan koordinat akhir dilatasinya? Koordinat akhir bisa dicari dengan persamaan matriks berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"298\" height=\"80\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/02\/bagaimana-cara-menentukan-koordinat-akhir-dilatasinya-Koordinat-akhir-bisa-dicari-dengan-persamaan-matriks-berikut..webp\" alt=\"\" class=\"wp-image-313300\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Agar kamu semakin paham, yuk simak contoh soalnya.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Suatu segitiga ABC memiliki titik koordinat sebagai berikut.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Titik A = (4, 6)<\/li>\n\n\n\n<li>Titik B = (2, 2)<\/li>\n\n\n\n<li>Titik C = (6, 2)<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Jika segitiga tersebut didilatasi terhadap titik pusat (2, -2) dengan faktor pengali = -1\/2, tentukan gambar objek beserta hasil dilatasinya!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Sebelum mengeplot titik A, B, dan C pada koordinat Cartesius, sebaiknya tentukan dulu koordinat hasil dilatasinya, ya.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Koordinat titik A\u2019<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Diketahui titik A (4, 6), k = -1\/2<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"374\" height=\"307\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/02\/Diketahui-titik-A-4-6-k.webp\" alt=\"\" class=\"wp-image-313302\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Dengan demikian, A\u2019 = (1, -6).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Koordinat titik B\u2019<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Diketahui titik B (2, 2), k = -1\/2<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"383\" height=\"306\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/02\/Diketahui-titik-B-2-2-k.webp\" alt=\"\" class=\"wp-image-313304\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Dengan demikian, B\u2019 = (2, -4).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Koordinat titik C\u2019<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Diketahui titik C (6, 2), k = -1\/2<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"370\" height=\"305\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/02\/Diketahui-titik-C-6-2-k.webp\" alt=\"\" class=\"wp-image-313307\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Dengan demikian, C\u2019 = (0, -4).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Jika titik-titik tersebut disubstitusikan ke dalam koordinat Cartesius, akan diperoleh gambar seperti berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"617\" height=\"707\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/02\/titik-tersebut-disubstitusikan-ke-dalam-koordinat-Cartesius.webp\" alt=\"\" class=\"wp-image-313308\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Oleh karena faktor dilatasinya k = -1\/2, maka bayangan objeknya diperkecil dengan arah sudut dilatasi berlawanan terhadap sudut dilatasi semula.<\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Contoh Soal<\/h2>\n\n\n\n<p class=\"wp-block-paragraph\">Untuk mengasah pemahamanmu, yuk simak contoh soal seperti di bawah ini.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Contoh Soal 1<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Suatu titik Q (6,3) mengalami dilatasi terhadap pusat (3, -5). Jika faktor pengalinya -1, tentukan koordinat akhir titik Q.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Untuk mencari koordinat akhir titik Q, gunakan persamaan berikut ini.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"424\" height=\"299\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/02\/Untuk-mencari-koordinat-akhir-titik-Q-gunakan-persamaan-berikut-ini.webp\" alt=\"\" class=\"wp-image-313311\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Jadi, koordinat akhir titik Q atau titik Q\u2019 (-2, -6).<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Contoh Soal 2<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Suatu bangun persegi PQRS memiliki koordinat masing-masing seperti berikut.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Titik P(2,-2)<\/li>\n\n\n\n<li>Titik Q(4,-2)<\/li>\n\n\n\n<li>Titik R(2, -4)<\/li>\n\n\n\n<li>Titik S(4,-4)<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Bangun tersebut ditranslasikan terhadap titik pusat (0,0) dengan faktor pengali 3\/2. Gambarkan dilatasi bangun persegi PQRS tersebut!<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pembahasan:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Pertama, kamu harus menentukan koordinat akhir masing-masing titik.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Titik P\u2019<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"244\" height=\"189\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/02\/Contoh-Soal-Titik-P.webp\" alt=\"\" class=\"wp-image-313313\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Dengan demikian, koordinat titik P\u2019 = (3,-3).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Titik Q\u2019<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"235\" height=\"201\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/02\/contoh-soal-titik-q.webp\" alt=\"\" class=\"wp-image-313315\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Dengan demikian, koordinat titik Q\u2019 = (6,-3).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Titik R\u2019<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"237\" height=\"193\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/02\/contoh-soal-titik-r.webp\" alt=\"\" class=\"wp-image-313317\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Dengan demikian, koordinat titik R\u2019 = (3,-6).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>Titik S\u2019<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"213\" height=\"194\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/02\/contoh-soal-titik-s.webp\" alt=\"\" class=\"wp-image-313319\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Dengan demikian, koordinat titik R\u2019 = (6, -6).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Jika kedua bangun digambarkan dalam koordinat Cartesius, diperoleh gambar seperti berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"485\" height=\"379\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/02\/Jika-kedua-bangun-digambarkan-dalam-koordinat-Cartesius.webp\" alt=\"\" class=\"wp-image-313321\"\/><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">Contoh Soal 3<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Titik A yang berkoordinat (3, 9) mengalami dilatasi terhadap titik pusat (a, b) dengan faktor pengali 2, sehingga diperoleh koordinat akhir A\u2019 (5, 16). Tentukan koordinat titik pusat dilatasinya!<\/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\">x = 3<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">y = 9<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">k = 2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">x&#8217; =  5<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">y&#8217; =  16<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Ditanya: (a, b) =\u2026?<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Jawab:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Untuk menentukan titik pusat dilatasinya, gunakan persamaan dilatasi terhadap titik pusat (a, b) seperti berikut.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"336\" height=\"245\" src=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/02\/Untuk-menentukan-titik-pusat-dilatasinya-gunakan-persamaan-dilatasi-terhadap-titik-pusat-a-b-seperti-berikut..webp\" alt=\"\" class=\"wp-image-313324\"\/><\/figure>\n\n\n\n<p class=\"wp-block-paragraph\">Dari persamaan di atas, diperoleh:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">5 = 6 &#8211; 2a + a<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u21d4 a = 1<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">16 = 18 &#8211; 2b + b<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">\u21d4 b = 2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Dengan demikian, diperoleh a = 1 dan b = 2.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Jadi, koordinat titik pusat (a, b) adalah (1, 2).<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Itulah pembahasan Quipper Blog kali ini. Semoga bermanfaat, ya. Untuk mendapatkan materi lengkapnya, yuk buruan gabung Quipper Video. Salam Quipper!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Hai Quipperian, bagaimana kabarnya? Semoga selalu sehat, ya. Pernahkah kamu memanfaatkan tools zoom\/perbesaran saat sedang memfoto suatu objek? Jika kamu memperbesar suatu objek melalui&hellip;<\/p>\n","protected":false},"author":156742495,"featured_media":313328,"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":[679386821,679386836],"class_list":["post-313276","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>Rumus dan Jenis-Jenis Dilatasi Matematika serta Contoh Soal - Quipper Blog<\/title>\n<meta name=\"description\" content=\"Dilatasi adalah perubahan titik suatu objek pada bidang geometri berdasarkan nilai faktor pengalinya. 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Namun, bisa juga ukuran bayangannya tetap\" \/>\n<meta property=\"og:url\" content=\"https:\/\/quipperhome.wpcomstaging.com\/mapel\/matematika\/dilatasi-matematika\/\" \/>\n<meta property=\"og:site_name\" content=\"Quipper Blog\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/QuipperVideoID\/\" \/>\n<meta property=\"article:published_time\" content=\"2023-02-16T06:23:33+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2023-02-16T06:24:58+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2023\/02\/Rumus-dan-Jenis-Jenis-Dilatasi-Matematika-serta-Contoh-Soal.webp\" \/>\n\t<meta property=\"og:image:width\" content=\"1280\" \/>\n\t<meta property=\"og:image:height\" content=\"780\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/webp\" \/>\n<meta name=\"author\" content=\"Ahmad Nurhakim, Pamela Natasa, S.Pd.\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@quipper_id\" \/>\n<meta name=\"twitter:site\" content=\"@quipper_id\" \/>\n<meta name=\"twitter:label1\" content=\"Ditulis oleh\" \/>\n\t<meta name=\"twitter:data1\" content=\"Ahmad Nurhakim\" \/>\n\t<meta name=\"twitter:label2\" content=\"Estimasi waktu membaca\" \/>\n\t<meta name=\"twitter:data2\" content=\"5 menit\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/mapel\\\/matematika\\\/dilatasi-matematika\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/mapel\\\/matematika\\\/dilatasi-matematika\\\/\"},\"author\":{\"name\":\"Ahmad Hakim\",\"@id\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/#\\\/schema\\\/person\\\/e8949d86562428c8aa73a14c68a5963f\"},\"headline\":\"Rumus dan Jenis-Jenis Dilatasi Matematika serta Contoh Soal\",\"datePublished\":\"2023-02-16T06:23:33+00:00\",\"dateModified\":\"2023-02-16T06:24:58+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/mapel\\\/matematika\\\/dilatasi-matematika\\\/\"},\"wordCount\":938,\"publisher\":{\"@id\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/#organization\"},\"image\":{\"@id\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/mapel\\\/matematika\\\/dilatasi-matematika\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/wp-content\\\/uploads\\\/2023\\\/02\\\/Rumus-dan-Jenis-Jenis-Dilatasi-Matematika-serta-Contoh-Soal.webp\",\"articleSection\":[\"Matematika\"],\"inLanguage\":\"id\"},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/mapel\\\/matematika\\\/dilatasi-matematika\\\/\",\"url\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/mapel\\\/matematika\\\/dilatasi-matematika\\\/\",\"name\":\"Rumus dan Jenis-Jenis Dilatasi Matematika serta Contoh Soal - Quipper Blog\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/mapel\\\/matematika\\\/dilatasi-matematika\\\/#primaryimage\"},\"image\":{\"@id\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/mapel\\\/matematika\\\/dilatasi-matematika\\\/#primaryimage\"},\"thumbnailUrl\":\"https:\\\/\\\/quipperhome.wpcomstaging.com\\\/wp-content\\\/uploads\\\/2023\\\/02\\\/Rumus-dan-Jenis-Jenis-Dilatasi-Matematika-serta-Contoh-Soal.webp\",\"datePublished\":\"2023-02-16T06:23:33+00:00\",\"dateModified\":\"2023-02-16T06:24:58+00:00\",\"description\":\"Dilatasi adalah perubahan titik suatu objek pada bidang geometri berdasarkan nilai faktor pengalinya. 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