Question

The coordinates of the vertices of triangle ABC are A(-1,3), B(1,2) and C(-3,-1).

Answer 1

In order to prove the triangle is a right angled triangle we need to prove that the slope of the lines CA and BC  and AB have any  negative reciprocals.Lets find the slopes . 
AB=(-1,3), (1,2) slope of AB = 2-3/1-(-1)= -1/2 slope of AB is -1/2
BC = (1,2), (-3,1) slope of BC is 1-2/-3-1= -1/-4 slope of BC is 1/4
Slope of CA =(-3,1)(-1,3) slope of 3-1/-1-(-3)=-2/-2=1

Since the slopes do not have any negative reciprocals so the triangle is not a right angled triangle