Answer
Right triangle
Work Step by Step
You are given the 3 points: $(2,1), (-4,1), (-4,-3)$. Calculate the distance between each point first.
Distance(P1, P2) = $\sqrt {(2-(-4))^2+(1-1)^2}$
=$\sqrt {36}$
= $6$
Distance(P2, P3) = $\sqrt {(-4-(-4))^2+(1-(-3))^2}$
=$\sqrt {16}$
= $4$
Distance(P3, P1) = $\sqrt {(-4-2)^2+(-3-1)^2}$
=$\sqrt {52}$
= $2\sqrt {13}$
Since none of the sides are equal, this triangle is not isosceles. Instead, notice how the y-coordinates of P1 and P2 are both 1, and the x-coordinates of both P2 and P3 are -4, meaning this triangle is a right-angled triangle!
Another solution:
Calculate
$P_1P_2^2+P_2P_3^2=36+16=52$
$P_3P_1^2=52$
By the converse of the Pythagorean theorem, it means the triangle is a right triangle.
