Question

1- Calcule a distancia entre os pontos:

a) A(8,4) e B(-7,-4)

b)C(2,-5) e D(6,3)

Answer 1

$Fo\´rmula\to~~~~D_{ab}= \sqrt{(x_b-x_a)^2+(y_b-y_a)^2}$



$a)~~ A(8,4) ~~e ~~B(-7,-4) \\\\\\ D_{ab}= \sqrt{(-7-8)^2+(-4-4)^2}\to\\\\ D_{ab}= \sqrt{(-15)^2+(-8)^2}\to\\\\ D_{ab}= \sqrt{225+64}\to\\\\ D_{ab}= \sqrt{289}\to\\\\ \large\boxed{D_{ab}= 17}$





$b)~~C(2,-5)~~ e~~ D(6,3) \\\\\\ D_{cb}= \sqrt{(6-2)^2+(3-(-5))^2}\to\\\\ D_{cb}= \sqrt{4^2+(3+5)^2}\to\\\\ D_{cb}= \sqrt{4^2+8^2}\to\\\\ D_{cb}= \sqrt{16+64}\to\\\\ D_{cb}= \sqrt{80}\to \\\\D_{cb}= \sqrt{2^2.2^2.5}\to\\\\ D_{cb}= 2.2\sqrt{5}\to\\\\ \large\boxed{D_{cb}= 4 \sqrt{5} }$