Question

check whether the point (1,3) ,(-1,-1) ,(-2,-3) are collinear

Answer 1

=1/2[1(-1+3)+(-1)(-3-3)+(-2)(3+1)]
=1/2(2+6-8)
=1/2*0
=0

As area of the triangle is equal to 0 it is collinear....

Hope it helps u...

Answer 2

Let these points are vertices of a triangle. So the area of the triangle whose vertices are collinear is equal to 0. Therefore,
x1(y2-y3) +x2(y3-y1) +x3(y1-y2)
1[-1-(-3)]+(-1)(-3-3)+(-2)[3-(-1)]
-1+3-1(-6)-2(3+1)
2+6-8
6-6
=0
This verify that the points are collinear.
Hope this will help you