{"id":15906,"date":"2020-05-11T21:03:22","date_gmt":"2020-05-12T00:03:22","guid":{"rendered":"https:\/\/beduka.com\/blog\/?p=15906"},"modified":"2020-08-05T18:06:08","modified_gmt":"2020-08-05T21:06:08","slug":"o-que-sao-retas-perpendiculares","status":"publish","type":"post","link":"https:\/\/beduka.com\/blog\/materias\/matematica\/o-que-sao-retas-perpendiculares\/","title":{"rendered":"O que s\u00e3o retas perpendiculares? Tipos, defini\u00e7\u00e3o, \u00e2ngulos e f\u00f3rmula"},"content":{"rendered":"\n<p>Retas perpendiculares ocorrem quando o \u00e2ngulo formado entre elas vale 90\u00b0, ou seja, quando h\u00e1 um \u00e2ngulo reto. Elas s\u00e3o um tipo especial de retas concorrentes e existem duas formas de calcular se formar\u00e3o um \u00e2ngulo reto. Fique conosco para saber mais sobre o que s\u00e3o retas perpendiculares!<\/p>\n\n\n\n<p>Neste artigo sobre o que s\u00e3o retas perpendiculares, voc\u00ea encontrar\u00e1:<\/p>\n\n\n\n<ol><li>O que s\u00e3o retas e seus tipos (paralela, concorrente,etc)<\/li><li>O que s\u00e3o retas perpendiculares<\/li><li>Como saber se duas retas s\u00e3o perpendiculares<\/li><\/ol>\n\n\n\n<ul><li>Conhe\u00e7a nosso <a href=\"https:\/\/beduka.com\/blog\/dicas\/enem-dicas\/simulados-para-enem-online-e-gratuito\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\">Simulado gratuito<\/a>, que pode ser personalizado com as mat\u00e9rias que voc\u00ea mais precisa!<\/li><\/ul>\n\n\n\n<h2 class=\"wp-block-heading\">O que s\u00e3o retas&nbsp;<\/h2>\n\n\n\n<p>Para compreender o que s\u00e3o retas perpendiculares, \u00e9 necess\u00e1rio relembrarmos algumas <strong>caracter\u00edsticas das retas;<\/strong> isso nos <strong>ajudar\u00e1 a calcular algumas coisas adiante.<\/strong>&nbsp;<\/p>\n\n\n\n<ul><li>Se voc\u00ea <strong>j\u00e1 est\u00e1 com essa mat\u00e9ria fresquinha<\/strong>, pule para o<strong> pr\u00f3ximo t\u00f3pico<\/strong>!<\/li><\/ul>\n\n\n\n<p><strong>Retas s\u00e3o o conjunto de pontos infinitos<\/strong> e muito pr\u00f3ximos, <strong>formando uma linha<\/strong>. Elas podem estar nas posi\u00e7\u00f5es <strong>horizontal, vertical e inclinada; mas sempre possuem alguns elementos em comum<\/strong>.<\/p>\n\n\n\n<p>Na geometria, trabalhamos muito com o <strong>plano cartesiano, <\/strong>que \u00e9 o suporte no qual tra\u00e7amos as retas para analis\u00e1-las. <strong>Para tra\u00e7ar uma reta<\/strong> no plano cartesiano, \u00e9 importante ter, <strong>no m\u00ednimo, dois pontos que pertencem a essa reta. <\/strong>Esses pontos s\u00e3o <strong>coordenadas geogr\u00e1ficas<\/strong> e sua <strong>an\u00e1lise<\/strong> nos permitir\u00e1 tirar <strong>v\u00e1rias informa\u00e7\u00f5es das retas, inclusives de que tipo s\u00e3o.<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Tipos de reta<\/h3>\n\n\n\n<ul><li><strong>Retas paralelas:<\/strong> est\u00e3o lado a lado e n\u00e3o possuem nenhum ponto em comum.<\/li><li><strong>Retas coincidentes:<\/strong> possuem, no m\u00ednimo, dois pontos em comum. Uma est\u00e1 em cima da outra.<\/li><li><strong>Retas transversais:<\/strong> uma reta que, ao mesmo tempo, corta 2 ou mais retas diferentes.<\/li><li><strong>Retas concorrentes:<\/strong> duas retas diferentes que se cruzam em um \u00fanico ponto.<\/li><\/ul>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/05\/O-que-s\u00e3o-retas-perpendiculares-1.jpg\" alt=\"O que s\u00e3o retas perpendiculares - 1\" class=\"wp-image-15908\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/05\/O-que-s\u00e3o-retas-perpendiculares-1.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/05\/O-que-s\u00e3o-retas-perpendiculares-1-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/05\/O-que-s\u00e3o-retas-perpendiculares-1-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/div>\n\n\n\n<h2 class=\"wp-block-heading\">O que s\u00e3o retas Perpendiculares<\/h2>\n\n\n\n<p>Pois bem, como definimos anteriormente, <strong>retas perpendiculares s\u00e3o um tipo espec\u00edfico de retas concorrentes,<\/strong> em que o <strong>\u00e2ngulo formado entre elas deve ser, necessariamente, de 90\u00b0<\/strong>(\u00e2ngulo reto).<\/p>\n\n\n\n<p>Como se trata de 2 retas em um plano cartesiano, podemos dizer que h\u00e1 a forma\u00e7\u00e3o de 4 \u00e2ngulos retos.<strong> Normalmente desenhamos apenas um, pois os demais est\u00e3o impl\u00edcitos.<\/strong><\/p>\n\n\n\n<p>Para representar que duas retas r e s s\u00e3o perpendiculares entre si, utilizamos o s\u00edmbolo \u22a5. Assim, na imagem abaixo: <strong>r \u22a5 s, <\/strong>sendo que a intersec\u00e7\u00e3o se d\u00e1 no <strong>ponto P.<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/05\/O-que-s\u00e3o-retas-perpendiculares-2.jpg\" alt=\"O-que-s\u00e3o-retas-perpendiculares-2\" class=\"wp-image-15909\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/05\/O-que-s\u00e3o-retas-perpendiculares-2.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/05\/O-que-s\u00e3o-retas-perpendiculares-2-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/05\/O-que-s\u00e3o-retas-perpendiculares-2-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/div>\n\n\n\n<p><strong>Aten\u00e7\u00e3o:<\/strong> Retas perpendiculares tamb\u00e9m podem ser chamadas de <strong>retas ortogonais, <\/strong>significa <strong>a mesma coisa!<\/strong><\/p>\n\n\n\n<h2 class=\"wp-block-heading\">Como saber se duas retas s\u00e3o perpendiculares<\/h2>\n\n\n\n<p>Caso seja dada uma quest\u00e3o com o desenho de duas retas, sem afirmar o valor do \u00e2ngulo ou apontar o s\u00edmbolo no desenho, e se quer que <strong>prove a perpendicularidade; <\/strong>podemos fazer <strong>de<\/strong> <strong>duas maneiras:<\/strong><\/p>\n\n\n\n<ul><li>Pelo <strong>coeficiente angular <\/strong>(Geometria Anal\u00edtica, usando um pouco de <a rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\" href=\"https:\/\/beduka.com\/blog\/materias\/matematica\/o-que-e-seno-cosseno-e-tangente\/\" target=\"_blank\">Trigonometria)<\/a><\/li><li>Usando uma<strong> f\u00f3rmula<\/strong> simples (com base na <a href=\"https:\/\/beduka.com\/blog\/materias\/matematica\/funcao-de-1-grau\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\">fun\u00e7\u00e3o de primeiro grau<\/a>)<\/li><\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Usando f\u00f3rmula<\/h3>\n\n\n\n<p>A f\u00f3rmula \u00e9 um m\u00e9todo r\u00e1pido para sabermos se duas retas s\u00e3o perpendiculares entre si. No entanto, \u00e9 necess\u00e1rio que conhe\u00e7amos a <strong>equa\u00e7\u00e3o geral das retas, <\/strong>usando os <strong>coeficientes que acompanham x e y.<\/strong><\/p>\n\n\n\n<p>Se tivermos:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/05\/O-que-s\u00e3o-retas-perpendiculares-3.jpg\" alt=\"O-que-s\u00e3o-retas-perpendiculares-3\" class=\"wp-image-15910\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/05\/O-que-s\u00e3o-retas-perpendiculares-3.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/05\/O-que-s\u00e3o-retas-perpendiculares-3-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/05\/O-que-s\u00e3o-retas-perpendiculares-3-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/div>\n\n\n\n<p>Ent\u00e3o, com base nestas f\u00f3rmulas gerais da reta, podemos formar a igualdade que nos dar\u00e1 a <strong>nova f\u00f3rmula:<\/strong><\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/05\/O-que-s\u00e3o-retas-perpendiculares-4.jpg\" alt=\"O-que-s\u00e3o-retas-perpendiculares-4\" class=\"wp-image-15911\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/05\/O-que-s\u00e3o-retas-perpendiculares-4.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/05\/O-que-s\u00e3o-retas-perpendiculares-4-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/05\/O-que-s\u00e3o-retas-perpendiculares-4-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/div>\n\n\n\n<p>Assim, <strong>se o resultado for zero<\/strong>, significa que<strong> r e s s\u00e3o perpendiculares.<\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Coeficiente angular de retas perpendiculares<\/h3>\n\n\n\n<p>O <strong>coeficiente angular<\/strong> \u00e9 respons\u00e1vel por medir o <strong>grau de inclina\u00e7\u00e3o dessas retas, em rela\u00e7\u00e3o ao eixo x <\/strong>(abscissas), e o indicaremos com o<strong> s\u00edmbolo (m).<\/strong><\/p>\n\n\n\n<p>Portanto, se tivermos duas retas R e S, que se encontram no ponto A, podemos indicar seus coeficientes como m(s) e m(r), veja:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/05\/O-que-s\u00e3o-retas-perpendiculares-5.jpg\" alt=\"O-que-s\u00e3o-retas-perpendiculares-5\" class=\"wp-image-15912\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/05\/O-que-s\u00e3o-retas-perpendiculares-5.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/05\/O-que-s\u00e3o-retas-perpendiculares-5-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/05\/O-que-s\u00e3o-retas-perpendiculares-5-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/div>\n\n\n\n<p>Pelo estudo da geometria anal\u00edtica, \u00e9 poss\u00edvel dizer que <strong>duas retas perpendiculares ter\u00e3o os seus coeficientes angulares opostos e inversos, <\/strong>o que significa:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/05\/O-que-s\u00e3o-retas-perpendiculares-6.jpg\" alt=\"O-que-s\u00e3o-retas-perpendiculares-6\" class=\"wp-image-15913\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/05\/O-que-s\u00e3o-retas-perpendiculares-6.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/05\/O-que-s\u00e3o-retas-perpendiculares-6-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/05\/O-que-s\u00e3o-retas-perpendiculares-6-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/div>\n\n\n\n<ul><li>Para os curiosos: de onde veio isso? Vejamos:<\/li><\/ul>\n\n\n\n<p>1- Para calcular o coeficiente angular precisamos ter a fun\u00e7\u00e3o da reta, ou usar de geometria anal\u00edtica para ach\u00e1-la com base no plano cartesiano. <strong>Como fazer isso, voc\u00ea encontra no artigo sobre o que \u00e9 <\/strong><a href=\"https:\/\/beduka.com\/blog\/materias\/matematica\/funcao-de-1-grau\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\">fun\u00e7\u00e3o de primeiro grau.<\/a><\/p>\n\n\n\n<p>Depois que temos o valor de \u201ca\u201d, <strong>basta calcular sua tangente para encontrar o valor de \u201cm\u201d. <\/strong>Sendo \u201ca\u201d o termo pertencente \u00e0 fun\u00e7\u00e3o que descreve retas (y = ax + b), a f\u00f3rmula utilizada para calcular o coeficiente angular (m) de uma reta \u00e9:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/05\/f\u00f3rmula-coeficiente-de-angula\u00e7\u00e3o.jpg\" alt=\"f\u00f3rmula-coeficiente-de-angula\u00e7\u00e3o\" class=\"wp-image-15914\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/05\/f\u00f3rmula-coeficiente-de-angula\u00e7\u00e3o.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/05\/f\u00f3rmula-coeficiente-de-angula\u00e7\u00e3o-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/05\/f\u00f3rmula-coeficiente-de-angula\u00e7\u00e3o-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/div>\n\n\n\n<p>2- Atrav\u00e9s da geometria anal\u00edtica, e do desenho do plano cartesiano acima, podemos inferir que:<\/p>\n\n\n\n<div class=\"wp-block-image\"><figure class=\"aligncenter\"><img decoding=\"async\" loading=\"lazy\" width=\"600\" height=\"300\" src=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/05\/C\u00e1lculo-para-coeficiente-angular-de-retas-perpendiculares.jpg\" alt=\"C\u00e1lculo-para-coeficiente-angular-de-retas-perpendiculares\" class=\"wp-image-15915\" srcset=\"https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/05\/C\u00e1lculo-para-coeficiente-angular-de-retas-perpendiculares.jpg 600w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/05\/C\u00e1lculo-para-coeficiente-angular-de-retas-perpendiculares-300x150.jpg 300w, https:\/\/beduka.com\/blog\/wp-content\/uploads\/2020\/05\/C\u00e1lculo-para-coeficiente-angular-de-retas-perpendiculares-320x160.jpg 320w\" sizes=\"(max-width: 600px) 100vw, 600px\" \/><\/figure><\/div>\n\n\n\n<p>3-<strong> Resolvendo estes c\u00e1lculos<\/strong>, por meios das defini\u00e7\u00f5es de trigonometria, chegaremos \u00e0 afirma\u00e7\u00e3o que dissemos no in\u00edcio e que <strong>\u00e9 essencial ser guardada.<\/strong><\/p>\n\n\n\n<p>Gostou do nosso artigo sobre o que s\u00e3o retas perpendiculares? Confira <strong>outros artigos <\/strong>do nosso blog e <strong>se prepare para o Enem<\/strong> da melhor maneira! Voc\u00ea tamb\u00e9m pode se organizar com o nosso<a href=\"https:\/\/beduka.com\/blog\/dicas\/enem-dicas\/plano-de-estudos-gratuito\/\" target=\"_blank\" rel=\"noreferrer noopener\" aria-label=\" (abre numa nova aba)\"> plano de estudos<\/a>, o mais completo da internet, e o melhor: <strong>totalmente gratuito!<\/strong><\/p>\n\n\n\n<p>Queremos te ajudar a encontrar a FACULDADE IDEAL! Logo abaixo, fa\u00e7a uma pesquisa por curso e cidade que te mostraremos todas as faculdades que podem te atender. Informamos a nota de corte, valor de mensalidade, nota do MEC, avalia\u00e7\u00e3o dos alunos, modalidades de ensino e muito mais.<\/p>\n\n\n\n<p>Experimente agora!<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Retas perpendiculares ocorrem quando o \u00e2ngulo formado entre elas vale 90\u00b0, ou seja, quando h\u00e1 um \u00e2ngulo reto. Elas s\u00e3o um tipo especial de retas concorrentes e existem duas formas de calcular se formar\u00e3o um \u00e2ngulo reto. Fique conosco para saber mais sobre o que s\u00e3o retas perpendiculares! Neste artigo sobre o que s\u00e3o retas [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":15916,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_mi_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0},"categories":[487],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v20.10 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>O que s\u00e3o retas PERPENDICULARES? 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