To determine if three points are collinear or not determine the line passing through any two points and see if this line passes through the third point.

It has to be determined if the points (8, 6), (3, 4) and (1, -7) are collinear. First determine the equation of the line through (8, 6) and (3, 4). It is given by (y - 6)/(x - 8) = (4 - 6)/(3 - 8)

=> 5y - 30 = 2x - 16

=> 5y - 2x - 14 = 0

Substituting the coordinates of the third point (1, -7)

5*(-7) - 2*1 - 14

=> -35 - 2 - 14 = -51

This is not equal to 0.

**The three points are not collinear.**

For the line to be co-linear the determinant should be zero. that if (x1,y1),(x2.y2) and (x3,y3) are the three points then

**x1(y2-y3)+x2(y3-y1)+x3(y1-y2)=0**

now the three points are (8, 6), (3, 4) and (1, – 7) so

8(4-(-7))+3(-7-6)+1(6-4)

8*11+3*(-13)+2

=51 which is not equal to zero.

hence the three points are not collinear.