Question

What is the perimeter of POR with vertices p(-2,9) Q(7,-3) and R(-2,-3) in the coordinate plane

Answer 1

The perimeter of $\triangle PQR$ will be 36.

Explanation

Perimeter means the sum of all side lengths. So first we need to find the length of each side of the triangle using distance formula.

Given vertices of  $\triangle PQR$ are:  $P=(-2,9), Q=(7,-3)$ and $R=(-2,-3)$

Formula for distance between two points $(x_{1},y_{1})$ and $(x_{2}, y_{2})$ is:   $\sqrt{(x_{1}-x_{2})^2+(y_{1}-y_{2})^2}$

So, the length of side $PQ$ $=\sqrt{(-2-7)^2+(9+3)^2} =\sqrt{81+144}=\sqrt{225}=15$

the length of side $QR =\sqrt{(7+2)^2+(-3+3)^2}=\sqrt{81}=9$

and the length of side $PR =\sqrt{(-2+2)^2+(9+3)^2}=\sqrt{144}=12$

Thus, the perimeter of the triangle will be: $15+9+12= 36$