{"id":270,"date":"2023-07-10T01:42:26","date_gmt":"2023-07-10T01:42:26","guid":{"rendered":"https:\/\/mathority.org\/id\/rumus-jarak-antara-dua-titik-contoh-geometri-dan-latihan-soal-yang-diselesaikan\/"},"modified":"2023-07-10T01:42:26","modified_gmt":"2023-07-10T01:42:26","slug":"rumus-jarak-antara-dua-titik-contoh-geometri-dan-latihan-soal-yang-diselesaikan","status":"publish","type":"post","link":"https:\/\/mathority.org\/id\/rumus-jarak-antara-dua-titik-contoh-geometri-dan-latihan-soal-yang-diselesaikan\/","title":{"rendered":"Rumus jarak antara dua titik (geometri)"},"content":{"rendered":"<p>Di halaman ini Anda akan menemukan cara menghitung jarak antara dua titik dalam geometri (rumus). Anda juga akan dapat melihat contoh dan, sebagai tambahan, berlatih dengan latihan jarak antara dua titik yang telah diselesaikan. <\/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%bfcual-es-la-formula-de-la-distancia-entre-dos-puntos\"><\/span> Apa rumus jarak antara dua titik?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p> Jarak antara dua titik sama dengan panjang segmen yang menghubungkannya. Oleh karena itu, dalam matematika, untuk menentukan jarak antara dua titik yang berbeda, kita harus menghitung kuadrat selisih koordinatnya dan kemudian mencari akar dari jumlah kuadrat 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> Dengan kata lain rumus yang digunakan untuk menghitung jarak antara dua titik berbeda pada bidang kartesius adalah sebagai berikut: <\/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\"> Perhatikan koordinat dua titik 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-617b8c4c3becdf6f6f5ee619a5c8e9d7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(x_1,y_1) \\qquad \\qquad B(x_2,y_2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"209\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p style=\"text-align:left\"> <strong>Rumus jarak antara dua titik<\/strong> 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-db8fa011bbd9bef1ae4c02642919ea13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(A,B) = \\sqrt{(x_2-x_1)^2+(y_2-y_1)^2 \\vphantom{\\frac{1}{2}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"277\" style=\"vertical-align: -10px;\"><\/p>\n<\/p>\n<\/div>\n<p> Rumus ini berasal dari besaran suatu vektor. Sebenarnya yang kita lakukan dengan rumus ini sebenarnya adalah menghitung besaran vektor yang ditentukan oleh dua titik yang dimaksud. Anda dapat membaca lebih lanjut mengenai hal ini pada penjelasan <a href=\"https:\/\/mathority.org\/id\/modul-contoh-rumus-vektor-latihan-yang-diselesaikan\/\">apa itu modulus suatu vektor<\/a> .<\/p>\n<p> Sebaliknya, dalam geometri analitik, demonstrasi rumus jarak antara dua titik juga dapat dilakukan dengan menggunakan teorema Pythagoras: <\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-full is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/formule-geometrique-distance-entre-deux-points.webp\" alt=\"rumus jarak antara dua titik\" class=\"wp-image-5012\" width=\"329\" height=\"329\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<div class=\"adsb30\" style=\" margin:12px; text-align:center\">\n<div id=\"ezoic-pub-ad-placeholder-106\"><\/div>\n<\/div>\n<p> Teorema Pythagoras menyatakan bahwa kuadrat sisi miring suatu segitiga siku-siku sama dengan jumlah kuadrat kaki-kakinya, maka:<\/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-a030628d3e6320afdcc61fd4c3100ddd_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bigl(d(A,B)\\bigr)^2 = (x_2-x_1)^2 + (y_2-y_1)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"26\" width=\"280\" style=\"vertical-align: -7px;\"><\/p>\n<\/p>\n<p> Dan untuk mendapatkan rumusnya Anda hanya perlu mencari jarak antara 2 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-db8fa011bbd9bef1ae4c02642919ea13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(A,B) = \\sqrt{(x_2-x_1)^2+(y_2-y_1)^2 \\vphantom{\\frac{1}{2}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"277\" style=\"vertical-align: -10px;\"><\/p>\n<\/p>\n<p> Terakhir, perlu dicatat bahwa, jika kita bekerja dengan 3 titik koordinat, rumus jarak antara dua titik dalam ruang (dalam R3) akan sama tetapi menambahkan koordinat Z: <\/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-236a06c21ada3a9557cf73a29f47d8e7_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(A,B) = \\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2 \\vphantom{\\frac{1}{2}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"374\" style=\"vertical-align: -10px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejemplo-de-como-calcular-la-distancia-entre-dos-puntos\"><\/span> Contoh penghitungan jarak antara dua titik <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> Setelah kita melihat definisi rumus jarak antara dua titik, sekarang mari kita lihat cara menentukan jarak tersebut dengan menggunakan contoh:<\/p>\n<ul>\n<li> Tentukan jarak antara dua titik berikut:<\/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-cdf7bd1545cb6d04a4bb3851c6794466_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(-1,7) \\qquad \\qquad B(3,4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"190\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p> Untuk mencari jarak antara dua titik secara geometris, cukup terapkan rumus:<\/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-db8fa011bbd9bef1ae4c02642919ea13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(A,B) = \\sqrt{(x_2-x_1)^2+(y_2-y_1)^2 \\vphantom{\\frac{1}{2}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"277\" style=\"vertical-align: -10px;\"><\/p>\n<\/p>\n<p> Sekarang kita substitusikan koordinat titik-titik tersebut ke dalam rumus:<\/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-02a4310cdfe1552b81816867261a17fe_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(A,B) = \\sqrt{(3-(-1))^2+(4-7)^2 \\vphantom{\\frac{1}{2}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"271\" style=\"vertical-align: -10px;\"><\/p>\n<\/p>\n<p> Dan kami melakukan perhitungan:<\/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-4e48600907e65f89fb9be0d55a2d3b3a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} d(A,B)  &amp;= \\sqrt{(3+1)^2+(4-7)^2 \\vphantom{\\frac{1}{2}}} \\\\[2ex] &amp;= \\sqrt{4^2+(-3)^2 \\vphantom{\\frac{1}{2}}} \\\\[2ex] &amp;= \\sqrt{16+9}\\\\[2ex] &amp;= \\sqrt{25}\\\\[2ex] &amp; = \\bm{5}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"233\" width=\"244\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<p> Oleh karena itu, jarak antara dua titik sama dengan 5 satuan.<\/p>\n<p> Tentunya nilai jarak harus selalu memberikan tanda positif, karena jarak selalu positif. Jika tidak, berarti kita melakukan kesalahan dalam satu langkah. <\/p>\n<h2 class=\"wp-block-heading\"><span class=\"ez-toc-section\" id=\"ejercicios-resueltos-de-la-distancia-entre-dos-puntos\"><\/span> Mengatasi masalah jarak antara dua titik<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<h3 class=\"wp-block-heading\"> Latihan 1<\/h3>\n<p> Hitunglah jarak antara 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-aa5be81901d5be989c5b72facdd42354_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(4,2) \\qquad \\qquad B(1,5)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"177\" 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 solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Untuk mencari jarak geometri antara dua titik, cukup gunakan rumus:<\/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-db8fa011bbd9bef1ae4c02642919ea13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(A,B) = \\sqrt{(x_2-x_1)^2+(y_2-y_1)^2 \\vphantom{\\frac{1}{2}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"277\" style=\"vertical-align: -10px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang kita substitusikan koordinat titik-titik tersebut ke dalam rumus:<\/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-4afec52bf1fdc3c32a004a86e312b164_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(A,B) = \\sqrt{(1-4)^2+(5-2)^2 \\vphantom{\\frac{1}{2}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"244\" style=\"vertical-align: -10px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan kami melakukan perhitungan: <\/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-81d70676cabdc2985f2ebe7b88c54e2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} d(A,B) &amp; = \\sqrt{(-3)^2+3^2 } \\\\[2ex] &amp; = \\sqrt{9+9 } \\\\[2ex] &amp; = \\bm{\\sqrt{18}} \\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"108\" width=\"183\" style=\"vertical-align: 0px;\"><\/p>\n<\/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> Tentukan jarak antara 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-9b2fed9d7325f254ded1553b488d7a0b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(8,6) \\qquad \\qquad B(-4,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"190\" 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 solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Untuk mencari jarak matematis antara dua titik, kita harus menggunakan rumus yang sesuai:<\/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-db8fa011bbd9bef1ae4c02642919ea13_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(A,B) = \\sqrt{(x_2-x_1)^2+(y_2-y_1)^2 \\vphantom{\\frac{1}{2}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"277\" style=\"vertical-align: -10px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Sekarang kita substitusikan koordinat titik-titik tersebut ke dalam rumus:<\/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-5d1814bdae0e934c17e4d699ba2223c3_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(A,B) = \\sqrt{(-4-8)^2+(1-6)^2 \\vphantom{\\frac{1}{2}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"258\" style=\"vertical-align: -10px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan kami melakukan perhitungan: <\/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-1c9f9f5c93377868a352891d5b09630a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{aligned} d(A,B)  &amp;= \\sqrt{(-12)^2+(-5)^2 } \\\\[2ex] &amp;= \\sqrt{144+25 }\\\\[2ex] &amp;= \\sqrt{169} \\\\[2ex] &amp;= \\bm{13}\\end{aligned}\" title=\"Rendered by QuickLaTeX.com\" height=\"149\" width=\"219\" style=\"vertical-align: 0px;\"><\/p>\n<\/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> Hitung keliling segitiga yang dibentuk oleh titik A, B dan C seperti terlihat pada grafik di bawah ini: <\/p>\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\/exercice-resolu-de-distance-entre-deux-points.webp\" alt=\"menyelesaikan latihan jarak antara dua titik\" class=\"wp-image-3913\" width=\"338\" height=\"267\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\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 solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Pertama, kita perlu mengidentifikasi koordinat X dan Y setiap titik pada grafik: <\/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-9a16d799fdc0fa3c371c35ba5f0f3a3c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(2,1)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"52\" 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-df310f6e38e3e91250838800e5366e54_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"B(4,4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"53\" 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-68d3d057862c60995dc725a90e942df4_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"C(6,2)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"53\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan sekarang kita perlu menghitung jarak antara semua titik dengan rumus: <\/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-1854b638ed0238a7b80632324e67ae0f_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(A,B) = \\sqrt{(4-2)^2+(4-1)^2 } = \\sqrt{4+9} =\\sqrt{13} = 3,61\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"435\" style=\"vertical-align: -6px;\"><\/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-741fa87cdc51782a0770cd384048b8fb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(A,C) = \\sqrt{(6-2)^2+(2-1)^2 } = \\sqrt{16+1} =\\sqrt{17} = 4,12\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"443\" style=\"vertical-align: -6px;\"><\/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-79954ecf2f51f8c6e230b15c56dfd2f6_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(B,C) = \\sqrt{(6-4)^2+(2-4)^2 } = \\sqrt{4+4} =\\sqrt{8} = 2,83\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"427\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Jadi keliling segitiga sama dengan jumlah panjang ketiga sisinya: <\/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-9cdb85214a73df4e8a7e7ee238c1bc55_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P=3,61+4,12+2,83= \\bm{10,56}\" title=\"Rendered by QuickLaTeX.com\" height=\"17\" width=\"251\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\">Latihan 4<\/h3>\n<p> Periksa apakah segitiga yang titik sudutnya adalah titik A, B, dan C merupakan segitiga sama kaki. Tapi 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-df719532b223037ad6a672c50a294c3d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(-4,5) \\qquad B(7,-5) \\qquad C(10,0)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"266\" 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 solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Agar segitiga sama kaki, dua sisinya harus sama panjang. Oleh karena itu, kita harus mencari panjang masing-masing sisinya, yang sesuai dengan jarak antara titik sudutnya.<\/p>\n<p class=\"has-text-align-left\"> Oleh karena itu kami menghitung jarak antara titik sudut segitiga: <\/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-786e56f8fe183e8143b1fb4f7f616226_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(A,B) = \\sqrt{(7-(-4))^2+(-5-5)^2 } = \\sqrt{11^2+(-10)^2} = \\sqrt{221}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"492\" style=\"vertical-align: -6px;\"><\/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-61cea14c48c09e4b4ae79b45d78cb746_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(A,C) = \\sqrt{(10-(-4))^2+(0-5)^2 } = \\sqrt{14^2+(-5)^2}  = \\sqrt{221}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"477\" style=\"vertical-align: -6px;\"><\/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-008513f83c089a4f9d4bc62b48a02aae_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(B,C) = \\sqrt{(10-7)^2+(0-(-5))^2} = \\sqrt{3^2+5^2} = \\sqrt{34}\" title=\"Rendered by QuickLaTeX.com\" height=\"22\" width=\"430\" style=\"vertical-align: -6px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Jadi segitiga tersebut mempunyai 2 sisi yang identik dan ukuran sisi ketiganya berbeda dari dua sisi lainnya, maka segitiga tersebut sebenarnya merupakan segitiga sama kaki.<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<h3 class=\"wp-block-heading\"> Latihan 5<\/h3>\n<p> Temukan sebuah titik pada sumbu Y yang berjarak sama dari 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-94ff2ed3e9145831e9919ad74a4d4c4c_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"A(5,-3) \\qquad \\qquad B(-2,4)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"204\" 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 solusi<\/strong><\/div>\n<\/div>\n<p class=\"has-text-align-left\"> Pertama-tama, jika suatu titik terletak pada sumbu komputer (sumbu OY) berarti absis titik tersebut adalah nol:<\/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-5cde05cd2f5f74f5290621fdbe275415_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"P(0,y)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"53\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Kedua, jika titik tersebut berjarak sama dari titik A dan B, maka persamaan berikut terpenuhi:<\/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-26224760f49fac42cea9d39dfe53dd4a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"d(P,A)= d(P,B)\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"136\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Jadi, dengan menggunakan rumus jarak antara dua titik, kita dapat mencari nilai variabel <em>y<\/em> dari persamaan sebelumnya:<\/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-8a5f1368ddd79fe90319f21cc904d392_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\sqrt{(5-0)^2+(-3-y)^2 \\vphantom{\\frac{1}{2}}}=\\sqrt{(-2-0)^2+(4-y)^2 \\vphantom{\\frac{1}{2}}}\" title=\"Rendered by QuickLaTeX.com\" height=\"32\" width=\"374\" style=\"vertical-align: -10px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Karena kedua ruas persamaan mempunyai akar, kita dapat menyederhanakannya:<\/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-26c1085f06beb112f73bac79ec7a7a2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"5^2+(-3-y)^2=(-2)^2+(4-y)^2\" title=\"Rendered by QuickLaTeX.com\" height=\"20\" width=\"264\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Kami menyelesaikan kekuatan dan persamaan penting (atau produk penting):<\/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-59f4cfbad3f47e15ec8dd45d8eff5b0e_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"25+9+y^2+6y=4+16+y^2-8y\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"277\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Dan kami beroperasi sampai kami menemukan nilai yang tidak diketahui <em>y<\/em> : <\/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-1e112c8e3a8ff239195ad850bd0e3f55_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y^2+6y-y^2+8y=4+16-25-9\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"277\" style=\"vertical-align: -4px;\"><\/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-dc1582050e8015be81566a4ba06585ea_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"14y=-14\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"82\" style=\"vertical-align: -4px;\"><\/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-67e3c61051e1e6f4d5ae83c0a7f8f51a_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=\\cfrac{-14}{14}\" title=\"Rendered by QuickLaTeX.com\" height=\"38\" width=\"75\" 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-9f371b4e77462e28d9f6119571c92982_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"y=-1\" title=\"Rendered by QuickLaTeX.com\" height=\"16\" width=\"55\" style=\"vertical-align: -4px;\"><\/p>\n<\/p>\n<p class=\"has-text-align-left\"> Singkatnya, poin dari pernyataan masalah yang ditanyakan kepada kami 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-5d1dd065d80d8fce8e53869201ad7b2b_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\bm{P(0,-1)}\" title=\"Rendered by QuickLaTeX.com\" height=\"19\" width=\"66\" style=\"vertical-align: -5px;\"><\/p>\n<\/p>\n<div class=\"wp-block-otfm-box-spoiler-end otfm-sp_end\"><\/div>\n<p> Jika Anda merasa artikel ini bermanfaat, Anda mungkin juga tertarik dengan <a href=\"https:\/\/mathority.org\/id\/jarak-antara-titik-dan-garis-contoh-rumus-soal-soal-yang-diselesaikan\/\">latihan jarak antara titik dan garis<\/a> . Pada halaman tertaut Anda tidak hanya akan menemukan latihan yang diselesaikan selangkah demi selangkah, tetapi juga penjelasan rinci tentang menghitung jarak antara titik dan garis, contoh dan penerapan rumus jarak antara titik dan garis untuk menentukan jenis jarak lainnya. .<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Di halaman ini Anda akan menemukan cara menghitung jarak antara dua titik dalam geometri (rumus). Anda juga akan dapat melihat contoh dan, sebagai tambahan, berlatih dengan latihan jarak antara dua titik yang telah diselesaikan. Apa rumus jarak antara dua titik? Jarak antara dua titik sama dengan panjang segmen yang menghubungkannya. Oleh karena itu, dalam matematika, &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/id\/rumus-jarak-antara-dua-titik-contoh-geometri-dan-latihan-soal-yang-diselesaikan\/\"> <span class=\"screen-reader-text\">Rumus jarak antara dua titik (geometri)<\/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-270","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>Rumus jarak antara dua titik (geometri) - Mathority<\/title>\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\/rumus-jarak-antara-dua-titik-contoh-geometri-dan-latihan-soal-yang-diselesaikan\/\" \/>\n<meta property=\"og:locale\" content=\"id_ID\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Rumus jarak antara dua titik (geometri) - Mathority\" \/>\n<meta property=\"og:description\" content=\"Di halaman ini Anda akan menemukan cara menghitung jarak antara dua titik dalam geometri (rumus). Anda juga akan dapat melihat contoh dan, sebagai tambahan, berlatih dengan latihan jarak antara dua titik yang telah diselesaikan. Apa rumus jarak antara dua titik? Jarak antara dua titik sama dengan panjang segmen yang menghubungkannya. 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Mathority","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathority.org\/id\/rumus-jarak-antara-dua-titik-contoh-geometri-dan-latihan-soal-yang-diselesaikan\/","og_locale":"id_ID","og_type":"article","og_title":"Rumus jarak antara dua titik (geometri) - Mathority","og_description":"Di halaman ini Anda akan menemukan cara menghitung jarak antara dua titik dalam geometri (rumus). Anda juga akan dapat melihat contoh dan, sebagai tambahan, berlatih dengan latihan jarak antara dua titik yang telah diselesaikan. Apa rumus jarak antara dua titik? Jarak antara dua titik sama dengan panjang segmen yang menghubungkannya. Oleh karena itu, dalam matematika, &hellip; Rumus jarak antara dua titik (geometri) Selengkapnya &raquo;","og_url":"https:\/\/mathority.org\/id\/rumus-jarak-antara-dua-titik-contoh-geometri-dan-latihan-soal-yang-diselesaikan\/","article_published_time":"2023-07-10T01:42:26+00:00","og_image":[{"url":"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-617b8c4c3becdf6f6f5ee619a5c8e9d7_l3.png"}],"author":"Tim Mathority","twitter_card":"summary_large_image","twitter_misc":{"Ditulis oleh":"Tim Mathority","Estimasi waktu membaca":"3 menit"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathority.org\/id\/rumus-jarak-antara-dua-titik-contoh-geometri-dan-latihan-soal-yang-diselesaikan\/#article","isPartOf":{"@id":"https:\/\/mathority.org\/id\/rumus-jarak-antara-dua-titik-contoh-geometri-dan-latihan-soal-yang-diselesaikan\/"},"author":{"name":"Tim Mathority","@id":"https:\/\/mathority.org\/id\/#\/schema\/person\/ea4523caf53a07e2ebf32e306a925b38"},"headline":"Rumus jarak antara dua titik (geometri)","datePublished":"2023-07-10T01:42:26+00:00","dateModified":"2023-07-10T01:42:26+00:00","mainEntityOfPage":{"@id":"https:\/\/mathority.org\/id\/rumus-jarak-antara-dua-titik-contoh-geometri-dan-latihan-soal-yang-diselesaikan\/"},"wordCount":677,"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\/rumus-jarak-antara-dua-titik-contoh-geometri-dan-latihan-soal-yang-diselesaikan\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathority.org\/id\/rumus-jarak-antara-dua-titik-contoh-geometri-dan-latihan-soal-yang-diselesaikan\/","url":"https:\/\/mathority.org\/id\/rumus-jarak-antara-dua-titik-contoh-geometri-dan-latihan-soal-yang-diselesaikan\/","name":"Rumus jarak antara dua titik (geometri) - 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