Answer
Yes, this is a right triangle.
Work Step by Step
The distance between A and B:
$$\sqrt{(-2-0)^2+(-8-(-4))^2}$$
$$\sqrt{4+16}$$
$$\sqrt{20}$$
The distance between B and C:
$$\sqrt{(0-(-4))^2+(-4-(-7))^2}$$
$$\sqrt{16+9}$$
$$\sqrt{25}$$
The distance between C and D:
$$\sqrt{(-2-(-4))^2+(-8-(-7))^2}$$
$$\sqrt{4+1}$$
$$\sqrt{5}$$
Now, check that these three points form a right triangle using the Pythagorean Theorem.
$$20+5=25$$
$$25=25$$
Yes, this is a right triangle.