Question

2- Esboce os pontos abaixo no plano cartesiano e calcule a distância entre eles.
a) A = (3,7) e B = (1,4)
b) E = (3,-1) e F = (3,5)
c) H = (-2,-5) e 0 = (0,0)
d) M = (0,-2) e B = (5,-2). ?​

Answer 1

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☞ As distâncias são, respectivamente: √13, 6, √29 e 5. ✅

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

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☔ Oi, Eduardo. A distância entre dois pontos pode ser encontrada através da equação:

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$\large\red{\boxed{\pink{\boxed{\begin{array}{rcl} & & \\ & \orange{\rm d_{a, b} = \sqrt{(x_{b}  - x_{a})^{2}  + (y_{b}  - y_{a})^{2}} } & \\ & & \\ \end{array}}}}}$

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

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$\LARGE\blue{\sf d = \sqrt{(1 - 3)^2 + (4 - 7)^2} }$

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$\LARGE\blue{\sf d = \sqrt{(-2)^2 + (-3)^2} }$

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$\LARGE\blue{\sf d = \sqrt{4 + 9} }$

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$\Huge\green{\boxed{\rm~~~\gray{d}~\pink{=}~\blue{ \sqrt{13} }~~~}}$ ✅

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$\setlength{\unitlength}{0.95cm}\begin{picture}(6,5)\thicklines\put(0,0){\vector(1,0){5}}\put(0,0){\vector(0,1){5}}\put(0,0){\vector(-1,0){5}}\put(0,0){\vector(0,-1){5}}\put(4.8,0.2){x}\put(0.2,4.8){y}\put(1.0,3.50){\circle*{0.13}}\put(1.25,3.75){ \sf P_{A} }\put(0.50,2.0){\circle*{0.13}}\put(0.75,2.25){ \sf P_{B} }\bezier(1.0,3.50)(0.75,2.75)(0.50,2.0)\end{picture}$

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$\sf (Esta~imagem~n\tilde{a}o~\acute{e}~visualiz\acute{a}vel~pelo~App~Brainly$ ☹ )

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

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$\LARGE\blue{\sf d = \sqrt{(3 - 3)^2 + (5 - (-1))^2} }$

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$\LARGE\blue{\sf d = \sqrt{(0)^2 + (6)^2} }$

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$\LARGE\blue{\sf d = \sqrt{36} }$

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$\Huge\green{\boxed{\rm~~~\gray{d}~\pink{=}~\blue{ 6 }~~~}}$ ✅

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$\setlength{\unitlength}{0.95cm}\begin{picture}(6,5)\thicklines\put(0,0){\vector(1,0){5}}\put(0,0){\vector(0,1){5}}\put(0,0){\vector(-1,0){5}}\put(0,0){\vector(0,-1){5}}\put(4.8,0.2){x}\put(0.2,4.8){y}\put(1.50,-0.50){\circle*{0.13}}\put(1.75,-0.25){ \sf P_{E} }\put(1.50,2.50){\circle*{0.13}}\put(1.75,2.75){ \sf P_{F} }\bezier(1.50,-0.50)(1.50,1.0)(1.50,2.50)\end{picture}$

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$\sf (Esta~imagem~n\tilde{a}o~\acute{e}~visualiz\acute{a}vel~pelo~App~Brainly$ ☹ )

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

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$\LARGE\blue{\sf d = \sqrt{(0 - (-2))^2 + (0 - (-5))^2} }$

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$\LARGE\blue{\sf d = \sqrt{(2)^2 + (5)^2} }$

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$\LARGE\blue{\sf d = \sqrt{4 + 25} }$

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$\Huge\green{\boxed{\rm~~~\gray{d}~\pink{=}~\blue{ \sqrt{29} }~~~}}$ ✅

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$\setlength{\unitlength}{0.95cm}\begin{picture}(6,5)\thicklines\put(0,0){\vector(1,0){5}}\put(0,0){\vector(0,1){5}}\put(0,0){\vector(-1,0){5}}\put(0,0){\vector(0,-1){5}}\put(4.8,0.2){x}\put(0.2,4.8){y}\put(-1.0,-2.50){\circle*{0.13}}\put(-0.75,-2.25){ \sf P_{H} }\put(0.0,0.0){\circle*{0.13}}\put(0.25,0.25){ \sf P_{O} }\bezier(-1.0,-2.50)(-0.50,-1.25)(0.0,0.0)\end{picture}$

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$\sf (Esta~imagem~n\tilde{a}o~\acute{e}~visualiz\acute{a}vel~pelo~App~Brainly$ ☹ )

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

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$\LARGE\blue{\sf d = \sqrt{(5 - 0)^2 + (-2 - (-2))^2} }$

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$\LARGE\blue{\sf d = \sqrt{(5)^2 + 0^2} }$

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$\LARGE\blue{\sf d = \sqrt{25} }$

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$\Huge\green{\boxed{\rm~~~\gray{d}~\pink{=}~\blue{ 5 }~~~}}$ ✅

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$\setlength{\unitlength}{0.95cm}\begin{picture}(6,5)\thicklines\put(0,0){\vector(1,0){5}}\put(0,0){\vector(0,1){5}}\put(0,0){\vector(-1,0){5}}\put(0,0){\vector(0,-1){5}}\put(4.8,0.2){x}\put(0.2,4.8){y}\put(0.0,-1.0){\circle*{0.13}}\put(0.25,-0.75){ \sf P_{M} }\put(2.50,-1.0){\circle*{0.13}}\put(2.75,-0.75){ \sf P_{B} }\bezier(0.0,-1.0)(1.25,-1.0)(2.50,-1.0)\end{picture}$

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$\sf (Esta~imagem~n\tilde{a}o~\acute{e}~visualiz\acute{a}vel~pelo~App~Brainly$ ☹ )

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☔ Leia mais sobre:

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✈ Distância entre Dois Pontos (https://brainly.com.br/tarefa/37997846 )

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

Answer 2

Resposta:

Explicação passo-a-passo:

a) Distância entre A e B:

$\sqrt{(1-3)^{2} + (4-7)^2 } = \sqrt{(-2)^2 + (-3)^2} = \sqrt{4 + 9} = \sqrt{13}$

b) Distância entre E e F:

$\sqrt{(3-3)^{2} + (5- (-1))^2 } = \sqrt{0^2 + (6)^2} = \sqrt{0 + 36} = \sqrt{36} = 6$

c) Distância entre H e 0:

$\sqrt{(0-(2))^{2} + (0-(-5))^2 } = \sqrt{2^2 + 5^2} = \sqrt{4 + 25} = \sqrt{29}$

d) Distância entre M e B:

$\sqrt{(5-0)^{2} + (-2-(-2))^2 } = \sqrt{5^2 + 0^2} = \sqrt{25 + 0} = \sqrt{25} = 5$