Question

determine a distancia entre os pontos A e B,onde:(1/2, -1/3) , B (5/2) , (1/3)

Answer 1

$d_{\alpha\beta}= \sqrt{(x-x_o)^2+(y-y_o)^2}\\\\ d_{AB}= \sqrt{\left( \dfrac{5}{2}- \dfrac{1}{2}\right)^2+\left( \dfrac{1}{3}-\left(- \dfrac{1}{3}\right)\right)^2 }\\\\ d_{AB}= \sqrt{\left( \dfrac{4}{2}\right)^2+\left( \dfrac{1}{3}+ \dfrac{1}{3}\right)^2 }\\\\ d_{AB}= \sqrt{2^2+\left( \dfrac{2}{3}\right)^2 }\\\\ d_{AB}= \sqrt{4+ \dfrac{4}{9} }\\\\ d_{AB}= \sqrt{ \dfrac{40}{9} }\\\\ d_{AB}= \dfrac{ \sqrt{40} }{ \sqrt{9} }\\\\ d_{AB}= \dfrac{ \sqrt{2^2\cdot10} }{3}$

$\Large\boxed{d_{AB}= \dfrac{2 \sqrt{10} }{3}}$