Question

Are the point A ( 4,5 ) B (7,6) C ( 6,3) are collinear

Answer 1

Slope of AB = (6-5)/(7-4) = 1/3
Slope of BC = (3-6)/(6-7) = 3
Slope of AC = (3-5)/(6-4) = -1
It is clear that the slopes are unequal.
So the points are not collinear, they form a triangle.
Hope it may help you !!!!!

Answer 2

Answer:

If points are collinear, therefore

Area of triangle = 0

1/2{x1(y2-y3) + x2(y3-y1) + x3(y1- y2)=0

1/2{ 4(6-3) +7(3-5) +6(5-6) }=0

1/2{4(3) +7(-2) +6(-1) }=0

1/2{12-14-6}=0

1/2{ -8}=0

-4 =0

This implyies the points are not collinear.