Answer
Yes, this is a right triangle.
Work Step by Step
The distance between A and B:
$$\sqrt{(-7-6)^2+(4-(-2))^2}$$
$$\sqrt{169+36}$$
$$\sqrt{205}$$
The distance between B and C:
$$\sqrt{(6-0)^2+(-2-(-15))^2}$$
$$\sqrt{36+169}$$
$$\sqrt{205}$$
The distance between C and D:
$$\sqrt{(-7-0)^2+(4-(-15))^2}$$
$$\sqrt{49+361}$$
$$\sqrt{410}$$
Use the Pythagorean Theorem to see if this is a right triangle.
$$205+205=410$$
$$410=410$$
Yes, this is a right triangle.