Question

1. Dados os pontos abaixo, determine a distância entre eles.
a) A (-8, 4) e B (-5, -2)
b) C (-5, 4) e D (2, -5)

Answer 1

$d = \sqrt{(x - x_{0})^{2} + (y - y_{0})^{2} }\\d = \sqrt{(-8 - (-5))^{2} + (4 - (-2))^{2} }\\d = \sqrt{(-8+5)^{2} + (4 + 2)^{2} }\\d = \sqrt{(-3)^{2} + (6)^{2} }\\d = \sqrt{9 + 36 }\\d = \sqrt{9 + 36 }\\d = \sqrt{45 }\\d = 3\sqrt{5}$

$d = \sqrt{(x - x_{0})^{2} + (y - y_{0})^{2} }\\d = \sqrt{(-5 - 2)^{2} + (4 - (-5))^{2} }\\d = \sqrt{(-7)^{2} + (4+ 5)^{2} }\\d = \sqrt{49+ (9)^{2} }\\d = \sqrt{49+81}\\d = \sqrt{130}$