Question

em um plano cartesiano, há dois pontos e uma reta que une esses pontos. As coordenadas de um desses pontos é (3,8) e o coeficientes linear da reta é 20. Sabendo que o outro ponto tem coordenadas (-3,a), calcule a valor de a

Answer 1

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⠀⠀☞ O valor da coordenada 'a' é de -112. ✅

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⚡ " -Como encontramos o coeficiente angular de uma reta?"

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➡️⠀Dados dois pontos A e B pertencentes a esta reta podemos encontrá-lo através da equação:

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$\Large\red{\boxed{\pink{\boxed{\begin{array}{rcl}&&\\&\orange{\sf m = \dfrac{\Delta y}{\Delta x} = \dfrac{y_B - y_A}{x_B - x_A}}&\\&&\\\end{array}}}}}$

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$\text{\pink{ \Longrightarrow }~\Large\orange{ \sf m }}$ sendo o coeficiente angular da reta: a tangente do ângulo  formado entre a reta e o eixo das abscissas;

$\text{\pink{ \Longrightarrow }~\Large\orange{ \sf (x_A, y_A) }}$ sendo as coordenadas do ponto A;

$\text{\pink{ \Longrightarrow }~\Large\orange{ \sf (x_B, y_B) }}$ sendo as coordenadas do ponto B.

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$\setlength{\unitlength}{0.95cm}\begin{picture}(6,5)\thicklines\put(0,0){\vector(1,0){5}}\put(0,0){\vector(0,1){5}}\put(0,0){\vector(-1,0){5}}\put(0,0){\vector(0,-1){5}}\put(4.8,0.2){x}\put(0.2,4.8){y}\put(-3,1){\line(5,3){5}}\put(-3,1){\circle*{0.13}}\put(2,4){\circle*{0.13}}\put(2,1){\circle*{0.13}}\bezier{20}(2,4)(2,2.5)(2,1)\bezier{35}(-3,1)(-0.5,1)(2,1)\put(-3.7,1){\LARGE \sf A }\put(2.5,4){\LARGE \sf B }\put(2.3,2.4){\Large \sf \Delta y }\put(-1,0.4){\Large \sf \Delta x }\bezier(-2,1.55)(-1.7,1.5)(-1.7,1)\put(-2.3,1.1){ \sf \alpha }\end{picture}$

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$\Large\red{\boxed{\begin{array}{rcl}&\red{\underline{\footnotesize\sf Esta~imagem~n\tilde{a}o~\acute{e}~visualiz\acute{a}vel~pelo~App~Brainly.}}&\\&\green{\footnotesize\sf \bullet~Experimente~compartilhar\rightarrow copiar~e~acessar}&\\&\green{\footnotesize\sf o~link~copiado~pelo~seu~navegador~ou~Browser.}&\\\end{array}}}$

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➡️⠀Desta forma temos que:

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$\LARGE\blue{\sf 20 = \dfrac{a - 8}{-3 - 3}}$

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$\LARGE\blue{\sf 20 = -\dfrac{a - 8}{6}}$

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$\LARGE\blue{\sf (-6) \cdot 20 = a - 8}$

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$\LARGE\blue{\sf -120 = a - 8}$

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$\LARGE\blue{\sf a = 8 - 120}$  

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$\huge\green{\boxed{\rm~~~\gray{a}~\pink{=}~\blue{ -112 }~~~}}$ ✅

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$\bf\large\red{\underline{\quad\quad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}$☁

⠀⠀☀️ Leia mais sobre coeficiente angular de retas:

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$\bf\large\red{\underline{\quad\quad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}$☁

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