Answer
No, this is not a right triangle.
Work Step by Step
The distance between A and B:
$$\sqrt{(-4-1)^2+(1-4)^2}$$
$$\sqrt{25+9}$$
$$\sqrt{34}$$
The distance between B and C:
$$\sqrt{(1-(-6))^2+(4-(-1))^2}$$
$$\sqrt{49+25}$$
$$\sqrt{74}$$
The distance between C and D:
$$\sqrt{(-4-(-6))^2+(1-(-1))^2}$$
$$\sqrt{4+4}$$
$$\sqrt{8}$$
Now, check that these three points form a right triangle using the Pythagorean Theorem.
$$34+8=74$$
$$42\ne74$$
No, this is not a right triangle.
