Answer
Yes, this is a right triangle.
Work Step by Step
The distance between A and B:
$$\sqrt{(-4-2)^2+(3-5)^2}$$
$$\sqrt{36+4}$$
$$\sqrt{40}$$
The distance between B and C:
$$\sqrt{(2-(-1))^2+(5-(-6))^2}$$
$$\sqrt{9+121}$$
$$\sqrt{130}$$
The distance between A and c:
$$\sqrt{(-4-(-1))^2+(3-(-6))^2}$$
$$\sqrt{9+81}$$
$$\sqrt{90}$$
Use the Pythagorean Theorem to test if this is a right triangle.
$$40+90=130$$
$$130=130$$
Yes, this is a right triangle.