Show by section formula that the points (3,-2),(5,2)and (8,8) are collinear.

Asked by tarunkumardas32 | 5th Apr, 2019, 03:35: PM

Expert Answer:

We need to prove the points (3,-2),(5,2) and(8,8) are collinear.
A=(3,-2) B=(5,2) C=(8,8)
Let The points B divides AC in the ratio of k:1
Then the coordinates will be,
open parentheses fraction numerator 8 straight k plus 3 over denominator straight k plus 1 end fraction comma fraction numerator 8 straight k minus 2 over denominator straight k plus 1 end fraction close parentheses
Coordinates of B are (5,2)
Comparing we get,
fraction numerator 8 straight k plus 3 over denominator straight k plus 1 end fraction equals 5 space space and space fraction numerator begin display style 8 straight k minus 2 end style over denominator begin display style straight k plus 1 end style end fraction equals 2
8 straight k plus 3 equals 5 straight k plus 5 space space and space space 8 straight k minus 2 equals 2 straight k plus 2
straight k equals 2 over 3 space and space straight k equals 2 over 3
Value of k is same in both.
Therefore Points A,B,C are collinears.

Answered by Arun | 5th Apr, 2019, 04:27: PM