Answer
Isosceles right triangle
Work Step by Step
We are given the points:
$(1,-3)$
$(3,2)$
$(-2,4)$
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.
$d_1=\sqrt{(3-1)^2+[2-(-3)]^2}=\sqrt{29}$
$d_2=\sqrt{(-2-3)^2+(4-2)^2}=\sqrt{29}$
$d_3=\sqrt{(-2-1)^2+[4-(-3)]^2}=\sqrt{58}$
Compute $d_1^2+d_2^2$:
$d_1^2+d_2^2=(\sqrt{29})^2+(\sqrt {29})^2=29+29=58$
Compute $d_3^2$:
$d_3^2=(\sqrt{58})^2=58$
As $d_1^2+d_3^2=d_2^2$, the three sides verify the Pythagorean Theorem, so the triangle is a right triangle.
Because $d_1=d_2$, the triangle is isosceles.
