Question

calcule a distancia entre os pontos a(7, 10) e B (1, 2)

calcule a distancia entre os pontos a(1, 3) e B (8, 3)

calcule a distancia entre os pontos a(-2, 5) e B (-2, 1)

calcule a distancia entre os pontos a(4, 3) e B (10 , 3)

calcule a distancia entre os pontos a(1, 6) e B (-2, -5)

Answer 1

Utilizamos a seguinte fórmula para calcular a distância:

$\boxed{d = \sqrt{(X_{b}-X_{a})^{2}+(Y_{b}-Y_{a})^{2}}}$


Agora substituímos em cada caso:

a) $d = \sqrt{(X_{b}-X_{a})^{2}+(Y_{b}-Y_{a})^{2}} \\\\ d = \sqrt{(1-7)^{2}+(2-10)^{2}} \\\\ d = \sqrt{(-6)^{2}+(-8)^{2}} \\\\ d = \sqrt{36+64} \\\\ d =\sqrt{100} \\\\ \boxed{\boxed{d = 10}}$


b)$d = \sqrt{(X_{b}-X_{a})^{2}+(Y_{b}-Y_{a})^{2}} \\\\ d = \sqrt{(8-1)^{2}+(3-3)^{2}} \\\\ d = \sqrt{(7)^{2}+(0)^{2}} \\\\ d = \sqrt{49} \\\\ \boxed{\boxed{d =7}}$


c) $d = \sqrt{(X_{b}-X_{a})^{2}+(Y_{b}-Y_{a})^{2}} \\\\ d = \sqrt{(-2-(-2))^{2}+(1-5)^{2}} \\\\ d = \sqrt{(-2+2)^{2}+(1-5)^{2}} \\\\ d = \sqrt{(0)^{2}+(-4)^{2}} \\\\ d=\sqrt{16} \\\\ \boxed{\boxed{d =4}}$


d) $d = \sqrt{(X_{b}-X_{a})^{2}+(Y_{b}-Y_{a})^{2}} \\\\ d = \sqrt{(10-4)^{2}+(3-3)^{2}} \\\\ d = \sqrt{(6)^{2}+(0)^{2}} \\\\ d = \sqrt{36} \\\\ \boxed{\boxed{d = 6}}$


e) $d = \sqrt{(X_{b}-X_{a})^{2}+(Y_{b}-Y_{a})^{2}} \\\\ d = \sqrt{(-2-1)^{2}+(-5-6)^{2}} \\\\ d = \sqrt{(-3)^{2}+(-11)^{2}} \\\\ d = \sqrt{9+121} \\\\ \boxed{\boxed{d = \sqrt{130}}}$

Answer 2

vc sabe a formila pelo menos ner?  a(7,10) e b(1,2)
d=(xb-xa)²+(yb-ya)²
d=(1-7)²+(2-10)²
d=(-6)²+(-8)²
d=36+64
d=100
d=10