Question

Calcule a distância entre os pontos
M(1/2,-1/3) J(5/2, 1/3)

Answer 1

Utilizando a formula da distancia entre dois pontos:

$Distancia_{\,M,J}=\sqrt{(x_M-x_J)^2+(y_M-y_J)^2}\\\\\\Distancia_{\,M,J}=\sqrt{(\frac{1}{2}-\frac{5}{2})^2+(-\frac{1}{3}-\frac{1}{3})^2}\\\\\\Distancia_{\,M,J}=\sqrt{(-\frac{4}{2})^2+(-\frac{2}{3})^2}\\\\\\Distancia_{\,M,J}=\sqrt{\frac{16}{4}+\frac{4}{9}}\\\\\\Distancia_{\,M,J}=\sqrt{\frac{9~.~16~+~4~.~4}{36}}\\\\\\Distancia_{\,M,J}=\sqrt{\frac{144~+~16}{36}}\\\\\\Distancia_{\,M,J}=\sqrt{\frac{160}{36}}\\\\\\Distancia_{\,M,J}=\frac{1}{6}\sqrt{160}$

$Distancia_{\,M,J}=\frac{1}{6}\sqrt{4~.~4~.~10}\\\\\\Distancia_{\,M,J}=\frac{4}{6}\sqrt{10}\\\\\\\boxed{Distancia_{\,M,J}=\frac{2}{3}\sqrt{10}~\approx~2,11}$