(Q27)Verify that the points (1,5) (2,3) and (-2,-1) are collinear or not.

Answer

Given A(1,5) B(2,3) and C(-2,-1)

distance= √((x2 - x1)2 + (y2 - y1)2)

AB= √((-)2 + (-)2)

= √

BC= √((--)2 + (--)2)

= √

= √2

AC= √((--)2 + (--)2)

= √

Here the sum of no two segments is equal to third segment

Hence the points are not collinear

slope of AB,m1=
-5
-1
= -

slope of BC, m2=
--3
--2
=

m1≠m2

Hence A, B, C are not collinear.