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|=√((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|=√((7-(-2))^2+(9-3)^2)=√(9^2+6^2)=√(81+36)=√(117)\\\\=√(9\cdot13)=\sqrt9\cdot√(13)=3√(13)`