Question

Using the diagram below, determine what kind of triangle PQR is based on its sides.

Answer 1

The coordinates of the vertices of triangle are,

P(-4,2), Q(2,-5) and R(5,4).

Determine the length of side PQ by using distance formula.

$\begin{gathered} PQ=\sqrt[]{(2-(-4))^2+(-5-2)^2} \\ =\sqrt[]{(6)^2+(7)^2} \\ =\sqrt[]{36+49} \\ =\sqrt[]{85} \end{gathered}$

Determine the length of side PR by using distance formula.

$\begin{gathered} PR=\sqrt[]{(-4-5)^2+(2-4)^2} \\ =\sqrt[]{(-9)^2+(2)^2} \\ =\sqrt[]{81+4} \\ =\sqrt[]{85} \end{gathered}$

Determine the length of side QR by using distance formula.

$\begin{gathered} QR=\sqrt[]{(2-5)^2+(-5-4)^2} \\ =\sqrt[]{(3)^2+(-9)^2} \\ =\sqrt[]{9+81} \\ =\sqrt[]{90} \end{gathered}$

Since length of side PR and side PQ is equal to each. The triangle with two equal sides are called isosceles triangle.

So triangle PQR is isosceles triangle.