This question is Based on Section Formula Chapter of M.L Aggarwal book for ICSE BOARD for class 10.
Here you have to Show by section formula that the points given are collinear.
Solve this question.
This is the Question Number 29, Exercise 11 of M.L Aggarwal.
Deepak BoraNewbie
Show by section formula that the points (3, – 2), (5, 2) and (8, 8) are collinear.
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Let the point B(5,2) divides the line joining A(3,-2) and C(8,8) in the ratio m:n.
Then by section formula, x = (mx2+nx1)/(m+n)
5 = (m×8+n×3)/(m+n)
5 = (8m+3n)/(m+n)
5m+5n = 8m+3n
2n = 3m
m/n = 2/3 …(i)
By section formula, y = (my2+ny1)/(m+n)
2 = (m×8+n×-2)/(m+n)
2 = (8m-2n)/(m+n)
2m+2n = 8m-2n
6m = 4n
m/n = 4/6 = 2/3 …(ii)
Here ratios are same.
So the points are collinear.