Question

find the measure of a triangle if the vertices of triangle EFG are E(-3,3), F(1,-1), and G(-3,-5). then classify the triangle by its sides

Answer 1

EFG is a triangle with vertices

E(-3,3), F(1,-1) and G(-3,-5).

First, let us evaluate the length of each side of the triangle using the distanec formula.

`\begin{gathered} EF=\sqrt[]{(1+3)^2+(-1-3)^2} \\ =\sqrt[]{16+16} \\ =\sqrt[]{32} \\ =4\sqrt[]{2} \\ FG=\sqrt[]{(-3-1)^2+(-5+1)^2} \\ =\sqrt[]{16+16} \\ =4\sqrt[]{2} \\ EG=\sqrt[]{(-3+3)^2+(-5-3)^2} \\ =\sqrt[]{8^2} \\ =8 \end{gathered}`

Since two sides of the triangle are equal, therefore, EFG is an isoscele triangle.