For the triangle to be a right triangle there must be a pair adjacent sides which are at right angles to each other - that is whose slope product = -1.
Slope of AB = (4-2)/(-6- -3) = -2/3.
Slope of BC = (8-4)/ (1 - - 6) = 2/7
Slope of AC = (8-2) / (1 - -3) = 6/4 = 3/2.
Now 3/2 * -2/3 = -1 so sides AB and AC are at right angles and the 3 points are the vertices of a right triangle.
