Answer
$$\color {blue}{\bf\text{No, the points do not make a right triangle}}$$
Work Step by Step
For clarity lets start by naming our points:
$A=(-4,1)$
$B=(1,4)$
$C=(-6,-1)$
First, we'll use the distance formula to find the lengths of each side:
$d(P,Q)=\sqrt{(x_{P}-x_{Q})^2+(y_{P}-y_{Q})^2}$
$AB= \sqrt{(-4-1)^2+(1-4)^2}$
$AB= \sqrt{(-5)^2+(-3)^2}$
$AB= \sqrt{25+9}$
$AB= \sqrt{34}$
$AC= \sqrt{(-4-(-6))^2+(1-(-1))^2}$
$AC= \sqrt{(2)^2+(2)^2}$
$AC= \sqrt{4+4}$
$AC= \sqrt{8}$
$AC= 2\sqrt{2}$
$BC= \sqrt{(1-(-6))^2+(4-(-1))^2}$
$BC= \sqrt{7^2+5^2}$
$BC= \sqrt{49+25}$
$BC= \sqrt{74}$
Now that we have the lengths of the sides,
$AB=\sqrt{34} $, $AC=2\sqrt{2}$, $BC=\sqrt{74}$,
we can apply the Pythagorean Theorem $a^2+b^2=c^2$ to see if the sides make a right triangle.
$(\sqrt{34})^2+(2\sqrt{2})^2=(\sqrt{74})^2$
$34+4(2)=74$
$34+8=74$
$42=74$
Which is $\bf \text{false}$, so:
$$\color {blue}{\bf\text{No, the points do not make a right triangle}}$$
