{"id":130782,"date":"2017-05-26T13:10:48","date_gmt":"2017-05-26T06:10:48","guid":{"rendered":"https:\/\/video.quipper.com\/id\/blog\/?p=130782"},"modified":"2022-02-21T23:51:46","modified_gmt":"2022-02-21T16:51:46","slug":"matematika-dasar-sbmptn-tentang-transformasi","status":"publish","type":"post","link":"https:\/\/quipperhome.wpcomstaging.com\/masuk-ptn\/sbmptn\/matematika-sbmptn\/matematika-dasar-sbmptn-tentang-transformasi\/","title":{"rendered":"Matematika Dasar SBMPTN Tentang Transformasi"},"content":{"rendered":"<p><a href=\"http:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2017\/05\/f10ff-blog-image-matdas-sbmptn-transformasi-.jpg\" data-rel=\"penci-gallery-image-content\" ><img fetchpriority=\"high\" decoding=\"async\" class=\"aligncenter wp-image-130792\" src=\"http:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2017\/05\/f10ff-blog-image-matdas-sbmptn-transformasi-.jpg\" alt=\"Matematika Dasar SBMPTN Tentang Transformasi\" width=\"800\" height=\"521\" srcset=\"https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2017\/05\/f10ff-blog-image-matdas-sbmptn-transformasi-.jpg 796w, https:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2017\/05\/f10ff-blog-image-matdas-sbmptn-transformasi--768x500.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><br \/>\n<\/a><\/p>\n<p><span style=\"font-weight: 400;\">Quipperian! Tranformasi (perpindahan) yang dipelajari dalam matematika, antara lain translasi (pergeseran), refleksi (pencerminan), rotasi (perputaran), dan dilatasi (perbanyakan) sangat berguna untuk kalian perdalami lagi, khususnya jika kalian sedang dalam persiapan Matematika Dasar SBMPTN. <\/span><\/p>\n<p><span style=\"font-weight: 400;\">Karena, materi Transformasi sering keluar pada soal-soal SBMPTN sbelumnya. Hal yang sangat bermanfaat dalam mempelajari transformasi ini dalam pengembangannya adalah apabila transformasi itu dilakukan pada bidang koordinat Cartesius. <\/span><\/p>\n<p><span style=\"font-weight: 400;\">Oleh karena itu, untuk mempelajari materi dalam kegiatan belajar mengajar ini Anda harus memahami dengan baik tentang bidang koordinat Cartesius dan beberapa persamaan garis lurus yang istimewa, misalnya persamaan garis y = x, y = -x, y = 0, dan sebagainya.<\/span><\/p>\n<p>&nbsp;<\/p>\n<h2><b>Translasi dan Refleksi<\/b><\/h2>\n<p><b>1. Translasi (pergeseran)<\/b><\/p>\n<p><span style=\"font-weight: 400;\">Translasi adalah perpindahan suatu benda dari suatu tempat ke tempat lain dapat dilakukan dengan beberapa cara, antara lain dengan pergeseran, perputaran atau lainnya.<\/span><\/p>\n<p><a href=\"http:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2017\/05\/7d7eb-translasi.png\" data-rel=\"penci-gallery-image-content\" ><img decoding=\"async\" class=\"aligncenter wp-image-130802 size-full\" src=\"http:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2017\/05\/7d7eb-translasi.png\" alt=\"Matematika Dasar SBMPTN Tentang Transformasi\" width=\"452\" height=\"185\" \/><\/a><\/p>\n<p><span style=\"font-weight: 400;\">Misalnya suatu kubus dari A digeser sehingga menempati tempat B (Gambar 6.1). Dengan kata lain, perpindahan kubus dari A ke B dilakukan dengan pergeseran (translasi). Setelah pergeseran, kubus tidak berubah besar maupun bentuknya. <\/span><\/p>\n<p><a href=\"http:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2017\/05\/19d2b-sudut.png\" data-rel=\"penci-gallery-image-content\" ><img decoding=\"async\" class=\"aligncenter wp-image-130812 size-full\" src=\"http:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2017\/05\/19d2b-sudut.png\" alt=\"Matematika Dasar SBMPTN Tentang Transformasi\" width=\"344\" height=\"159\" \/><\/a><\/p>\n<p style=\"text-align: center;\"><span style=\"font-weight: 400;\">Pada Gambar 6.2, titik P digeser (ditranslasi) menjadi titik Q ditulis P -&gt; Q. <\/span><\/p>\n<p><span style=\"font-weight: 400;\">Titik P dapat pula digeser menjadi titik R atau duliskan P -&gt; R. Tampak di sini bahwa translasi P \u00a0-&gt; Q berbeda dengan translasi P \u00a0-&gt; R. Apakah perbedaan dua translasi ini. Perbedaan dua translasi itu terletak pada jarak pergeseran dan arah pergeserannya. Pada translasi P \u00a0-&gt; Q, jarak (panjang) pergeseran dinyatakan pleh panjang ruas garis PQ dan arah pergeseran dari P ke Q yang dinyatakan dengan arah anak panah. <\/span><br \/>\n<span style=\"font-weight: 400;\">Selanjutnya, panjang dan arah pergeseran pada translasi P \u00a0-&gt; Q dinyatakan dengan simbol PQ, PQ menyatakan besar (panjang) pergeseran dan anak panahnya menyatakan arah dari P menuju Q. Selanjutnya, PQ disebut vektor translasi.<\/span><\/p>\n<p><a href=\"http:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2017\/05\/0d53e-vektor-translasi.png\" data-rel=\"penci-gallery-image-content\" ><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-130822 size-full\" src=\"http:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2017\/05\/0d53e-vektor-translasi.png\" alt=\"Matematika Dasar SBMPTN Tentang Transformasi\" width=\"287\" height=\"302\" \/><\/a><\/p>\n<p><span style=\"font-weight: 400;\">Pada Gambar 6.3 \u2206 ABC ditranslasikan dengan vektor AD menjadi \u2206 DEF. Pada translasi ini, A \u00a0D, B \u00a0E, dan C \u00a0F sehingga vektor-vektor translasi AD , BE dan CF mempunyai besar (panjang) dan arah yang sama. Atau dikatakan AD = BE = CF<\/span><\/p>\n<h3 class=\"entry-title\"><a href=\"https:\/\/video.quipper.com\/id\/blog\/sbmptn\/informasi-sbmptn\/kisi-kisi-sbmptn-soshum-paling-update-dan-lengkap-untuk-persiapan-menuju-kampus-impian\/\" target=\"_blank\" rel=\"noopener\">Kisi-Kisi SBMPTN Soshum Paling Update dan Lengkap untuk Persiapan Menuju Kampus Impian!<\/a><\/h3>\n<p><span style=\"font-weight: 400;\">\u2206 DEF disebut bayangan (peta translasi) dari \u2206 ABC oleh translasi dengan vektor AD . Perhatikan bahwa hasil translasi, yaitu \u2206 DEF dan segitiga yang ditranslasikan, yaitu \u2206 ABC merupakan dua segitiga yang besar dan bentuknya (bangunannya) sama. Duan bangunan yang besar dan bentuknya sama dikatakan dua bangun yang kongruen (sama dan sebangun). <\/span><\/p>\n<p><span style=\"font-weight: 400;\">Pada gambar 6.3, translasi AB memetakan titik A ke B. Translasi BC memetakan titik B ke C. Translasi AB dilanjutkan dengan translasi BC memetakan titik A ke titik C. Translasi AB dilanjutkan dengan translasi BC di tulis translasi AB + BC , sedangkan translasi AC memetakan titik A ke titik C. Jadi, translasi AB + BC = <\/span><\/p>\n<p><span style=\"font-weight: 400;\">translasi AC ; AB + BC = AC <\/span><\/p>\n<p><span style=\"font-weight: 400;\">Suatu cara yang sangat berguna untuk menggambarkan suatu translasi adalah dengan suatu pasangan bilangan, yaitu apabila kita menggambarkannya pada bidang koordinat Cartesius.<\/span><\/p>\n<p><b>2. Refleksi (Pencerminan)<br \/>\n<\/b><br \/>\n<span style=\"font-weight: 400;\">Ketika kita sedang berkaca (bercermin) di belakang cermin tampak bayangan kita. Bayangan itu sama dengan kita baik bentuk maupun besarnya, perbedaannya terletak pada arahnya, yaitu berlawanan karena kita dan bayangan kita saling berhadapan.<br \/>\n<a href=\"http:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2017\/05\/0e34a-refleksi.png\" data-rel=\"penci-gallery-image-content\" ><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter wp-image-130832 size-full\" src=\"http:\/\/quipperhome.wpcomstaging.com\/wp-content\/uploads\/2017\/05\/0e34a-refleksi.png\" alt=\"Matematika Dasar SBMPTN Tentang Transformasi\" width=\"244\" height=\"262\" \/><\/a><\/span><\/p>\n<p><span style=\"font-weight: 400;\">Perhatikan Gambar 6.6, garis m dipandang sebagai cermin. Oleh cermin m ini, bayangan dari \u2206 ABC adalah \u2206 EFG. Dalam matematika, kita boleh pula mengatakan bahwa oleh cermin m bayangan dari \u2206 EFG adalah \u2206 ABC. Apabila pencerminan (refleksi) diberi simbol M maka pencerminan oleh garis m ditulis Mm Dengan pencerminan oleh garis m, bayangan \u2206 ABC adalah \u2206 EFG, ditulis dengan notasi Mm: \u2206 ABC = \u2206 EFG <\/span><\/p>\n<p><span style=\"font-weight: 400;\">Bangun (bentuk) dan besar benda dan bayangannya selalu sama sehingga benda dan bayangannya dikatakan sama dan sebangun (kongruen) yang diberi notasi \u201c~= \u201d. <\/span><\/p>\n<p><span style=\"font-weight: 400;\">Pada pencerminan Mm (Gambar 6.i), \u2206 ABC sama dan sebangun dengan \u2206 EFG (ditulis \u2206 ABC \u00a0\u2206 EFG). Bayangan titik B adalah titik F dan B = F. Suatu titik yang bayangannya titik itu sendiri disebut titik tetap (invarian). Jadi, titik B tersebut adalah suatu titik invarian sehingga Anda akan mengerti bahwa semua titik pada cermin merupakan titiktitik invarian. <\/span><\/p>\n<h3 class=\"entry-title\"><a href=\"https:\/\/video.quipper.com\/id\/blog\/sbmptn\/kimia\/soal-sbmptn-kimia-itu-gampang-nggak-percaya-ini-contoh-soal-latihan-beserta-pembahasannya\/\" target=\"_blank\" rel=\"noopener\">Soal SBMPTN Kimia Itu Gampang! Nggak Percaya? Ini Contoh Soal Latihan Beserta Pembahasannya!<\/a><\/h3>\n<p><span style=\"font-weight: 400;\">Jika titik A dan E dihubungkan, maka garis AE tegak lurus pada garis m (cermin). Tentukanlah bayangan garis AE terhadap cermin m!. Bayangan AD adalah ED dan bayangan ED adalah AD sehingga bayangan garis AE adalah garis EA. Padahal garis AE sam,a dengan garis EA maka mbayangan garis AE adalah garis itu sendiri. Selanjutnya dikatakan bahwa garis AE terhadap pencerminan dengan garis m merupakan garis tetap (garis invarian), tetapi tidak titik pertitik. <\/span><\/p>\n<p><span style=\"font-weight: 400;\"><strong>Penulis: Sritopia<\/strong><\/span><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Quipperian! Tranformasi (perpindahan) yang dipelajari dalam matematika, antara lain translasi (pergeseran), refleksi (pencerminan), rotasi (perputaran), dan dilatasi (perbanyakan) sangat berguna untuk kalian perdalami lagi,&hellip;<\/p>\n","protected":false},"author":156446345,"featured_media":130792,"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_feature_clip_id":0,"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[253044991],"tags":[169291195],"ppma_author":[679386822],"class_list":["post-130782","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-matematika-sbmptn","tag-contoh-soal-sbmptn"],"acf":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.6 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Matematika Dasar SBMPTN Tentang Transformasi<\/title>\n<meta name=\"description\" content=\"Quipperian, materi transformasi sering keluar di Matematika Dasar SBMPTN! 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