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

$Fo\´rmula~\to~~~~$



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





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