Answer
The triangle has two equal sides.
Work Step by Step
We are given the points:
$(2,3)$
$(4,9)$
$(-2,7)$
Determine the length of each side using the formula
$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$,
where $(x_1,y_1),(x_2,y_2)$ are the coordinates of the two points.
$d_1=\sqrt{(4-2)^2+(9-3)^2}=\sqrt{40}=2\sqrt{10}$
$d_2=\sqrt{(-2-4)^2+(7-9)^2}=\sqrt{40}=2\sqrt{10}$
$d_3=\sqrt{(-2-2)^2+(7-3)^2}=\sqrt{32}$
Because $d_1=d_2$, the triangle is isosceles.
