Question

Calcule a distância entre os pontos indicados:
a) A(-3;-5) e B(-3;7)
b) E(4;6) e F (9;18)

Answer 1

$\mathrm{d_{PQ}=\sqrt{(x_Q-x_P)^2+(y_Q-y_P)^2}}\\\\ \mathrm{\mathbf{a)}\ A(-3,-5)\ e\ B(-3,7)}\\\\ \mathrm{d_{AB}=\sqrt{(-3-(-3))^2+(7-(-5))^2}=}\\ \mathrm{=\sqrt{(-3+3)^2+(7+5)^2}=\sqrt{0^2+12^2}=}\\ \mathrm{=\sqrt{12^2}\ \to\ \boxed{\mathbf{d_{AB}=12\ u.c.}}}\\\\ \mathrm{\mathbf{b)}\ E(4,6)\ e\ F(9,18)}\\\\ \mathrm{d_{EF}=\sqrt{(9-4)^2+(18-6)^2}=}\\ \mathrm{=\sqrt{5^2+12^2}=\sqrt{25+144}=}\\ \mathrm{=\sqrt{169}\ \to\ \boxed{\mathbf{d_{EF}=13\ u.c.}}}$