Question

Sendo A = (−3; 2) e B = (5; −4) extremidades de um segmento, determinar:

A) os pontos C, D e E para que AC = CD =DE =EB.

B) os pontos F e G para que AF =FG =GB.

Answer 1

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☞ A) C = (-1, 0.5), D = (1, -1), E = (3, -2.5). ✅

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☞ B) F = (-0.3, 0) e G = (2.3, -2).✅

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$\green{\rm\underline{EXPLICAC_{\!\!\!,}\tilde{A}O\ PASSO{-}A{-}PASSO\ \ \ }}$✍

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☔ Oi, Thomas. Resolveremos este exercício analisando a distância entre os pontos A e B em cada coordenada:

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$\LARGE\blue{\sf d_x = x_b - x_a = 8 }$

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$\LARGE\blue{\sf d_y = y_b - y_a = -6 }$

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Ⓐ$\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad}}$✍

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☔ Dividiremos a distância em cada coordenada em 4 partes iguais:

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$\LARGE\blue{\sf \dfrac{d_x}{4} = \dfrac{8}{4} = 2 }$

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$\LARGE\blue{\sf \dfrac{d_y}{4} = \dfrac{-6}{4} = -1.5 }$

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$\Large\blue{\sf A = (-3, 2) }$

$\Large\blue{\sf C = (\overbrace{-3 + 2}^{\sf x_c}, \overbrace{2 + (-1.5)}^{\sf y_c}) = (-1, 0.5) }$  ✅

$\Large\blue{\sf D = (\overbrace{-1 + 2}^{\sf x_d}, \overbrace{0.5 + (-1.5)}^{\sf y_d}) = (1, -1) }$  ✅

$\Large\blue{\sf E = (\overbrace{1 + 2}^{\sf x_e}, \overbrace{-1 + (-1.5)}^{\sf y_e}) = (3, -2.5) }$  ✅

$\Large\blue{\sf B = (\overbrace{3 + 2}^{\sf x_b}, \overbrace{-2.5 + (-1.5)}^{\sf y_b}) = (5, -4) }$  

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Ⓑ$\bf\large\red{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\quad}}$✍

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☔ Dividiremos a distância em cada coordenada em 3 partes iguais:

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$\LARGE\blue{\sf \dfrac{d_x}{3} = \dfrac{8}{3} = 2.\overline{6} }$

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$\LARGE\blue{\sf \dfrac{d_y}{3} = \dfrac{-6}{3} = -2 }$

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$\Large\blue{\sf A = (-3, 2) }$

$\Large\blue{\text{ \sf F = (\overbrace{-3 + 2.\overline{6}}^{\sf x_f}, \overbrace{2 + (-2)}^{\sf y_f}) = (-0.\overline{3}, 0) }}$  ✅

$\Large\blue{\text{ \sf G = (\overbrace{-0.\overline{3} + 2.\overline{6}}^{\sf x_g}, \overbrace{0 + (-2)}^{\sf y_g}) = (2.\overline{3}, -2) }}$  ✅

$\Large\blue{\text{ \sf B = (\overbrace{2.\overline{3} + 2.\overline{6}}^{\sf x_b}, \overbrace{-2 + (-2)}^{\sf y_b}) = (5, -4) }}$  

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

☕ $\bf\Large\blue{Bons\ estudos.}$

($\orange{D\acute{u}vidas\ nos\ coment\acute{a}rios}$) ☄

$\bf\large\red{\underline{\qquad \qquad \qquad \qquad \qquad \qquad \quad }}\LaTeX$✍

❄☃ $\sf(\gray{+}~\red{cores}~\blue{com}~\pink{o}~\orange{App}~\green{Brainly})$ ☘☀

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$\gray{"Absque~sudore~et~labore~nullum~opus~perfectum~est."}$