Question

Determine a distância entre os pontos A e B nos seguintes casos:

A) a (-3,-1) e b (9,4)

B) a (-2,5) e b (4,-3)

Answer 1

$FO\´RMULA~\overrightarrow{~~~~~~}~~ D_{ab}= \sqrt{(x_b-x_a)^2+(y_b-y_a)^2}$



$A) ~~a~ (-3,-1)~~ e~~ b~ (9,4)\\\\D_{ab}= \sqrt{(9-(-3))^2+(4-(-1))^2}\to \\\\ D_{ab}= \sqrt{(9+3)^2+(4+1)^2}\to \\\\ D_{ab}= \sqrt{(12)^2+(5)^2}\to \\\\ D_{ab}= \sqrt{144+25}\to \\\\ D_{ab}= \sqrt{169}\to \\\\ \large\boxed{D_{ab}= 13}$



$B) ~~a~ (-2,5)~~ e~~ b~ (4,-3)\\\\D_{ab}= \sqrt{(4-(-2))^2+(-3-5)^2}\to \\\\ D_{ab}= \sqrt{(4+2)^2+(-8)^2}\to \\\\ D_{ab}= \sqrt{(6)^2+(-8)^2}\to \\\\ D_{ab}= \sqrt{36+64}\to \\\\ D_{ab}= \sqrt{100}\to \\\\ \large\boxed{D_{ab}= 10}$