Question

A segment has endpoints at (-2,3) and (7,9) , How Long is the segment

Answer 1

$\text{The formula of the distance between two points:}\\\\A(x_A;\ y_A);\ B(x_B;\ y_B)\\\\|AB|=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}$

$\text{We have:}\\A(-2;\ 3)\to x_A=-2;\ y_A=2\\B(7;\ 9)\to x_B=7;\ y_B=9\\\\\text{substitute}\\\\|AB|=\sqrt{(7-(-2))^2+(9-3)^2}=\sqrt{9^2+6^2}=\sqrt{81+36}=\sqrt{117}\\\\=\sqrt{9\cdot13}=\sqrt9\cdot\sqrt{13}=3\sqrt{13}$