Question

Distância entre dois pontos:
Coordenadas: A = (-4,4) e B = (3,4)

Answer 1

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⠀⠀⠀☞ A distância entre estes pontos, que estão alinhados horizontalmente, é de 7 [u.c.] ✅

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Como resolver?                              ✍

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⠀⠀⠀➡️⠀Oi, Kahu. Se analisarmos estes pontos em um plano cartesiano veremos que a distância entre eles forma a hipotenus de um triângulo retângulo de catetos paralelos aos eixos x e y. Pelo teorema de Pitágoras teremos então que:

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                            $\large\red{\boxed{\pink{\boxed{\begin{array}{rcl}&&\\&\orange{\sf d_{AB} = \sqrt[2]{\sf \Delta x^2 + \Delta y^2}}&\\&&\\&\Downarrow~~~~~~~~~~\Downarrow&\\&&\\&\orange{\sf d_{AB} = \sqrt[2]{\sf (x_B - x_A)^2 + (y_B - y_A)^2}}&\\&&\\\end{array}}}}}$

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d = √(-4 - 3)² + (4 - 4)²

d = √(-7)²

d = √49

d = 7 [u.c.]✅

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                             $\bf\large\purple{\underline{\qquad\qquad\qquad\qquad\qquad\qquad\qquad\qquad}}$⚪

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                             ⚡⠀https://brainly.com.br/tarefa/38693695⠀⚡

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                                     $\huge\blue{\text{\bf Bons~estudos.}}$ ☕

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$\orange{D\acute{u}vidas~sobre~a~resoluc_{\!\!,}\tilde{a}o?}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$\orange{Lanc_{\!\!,}a~nos~coment\acute{a}rios~!}$ ✌

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                             $\bf\large\pink{\underline{\qquad \qquad \qquad \qquad \qquad \qquad \quad }\LaTeX}$⭐

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀$\Huge\green{\text{ \underline{\red{\mathbb{S}}\blue{\mathfrak{oli}}~}~\underline{\red{\mathbb{D}}\blue{\mathfrak{eo}}~}~\underline{\red{\mathbb{G}}\blue{\mathfrak{loria}}~} }}$ ✞

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Answer 2

$\mathsf{ A(-4;4)\quad B(3;4)}$

$\mathsf{d_{AB}=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2} }$

$\mathsf{d_{AB}=\sqrt{(3-(-4))^2+(4-4) ^2}}$

$\mathsf{ d_{AB}=\sqrt{(7)^2+(0)^2}}$

$\mathsf{d_{AB}=\sqrt{49+0} }$

$\mathsf{ d_{AB}=\sqrt{49}}$

$\boxed{\boxed{\red{ \mathsf{d_{AB}=7}}} }$