An Important Question of M.L Aggarwal book of class 10 Based on Section Formula Chapter for ICSE BOARD.

In this question you have to find the value of p for which the given points are collinear.

This is the Question Number 30, Exercise 11 of M.L Aggarwal.

# Find the value of p for which the points ( – 5, 1), (1, p) and (4, – 2) are collinear.

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Let A(-5,1) divides the line joining (1,p) and (4,-2) in the ratio m:nThen by section formula,x = (mx_{2}+nx_{1})/(m+n)-5 = (m×4+n×1)/(m+n)-5 = (4m+n)/(m+n)-5m-5n = 4m+n-9m = 6nm/n = -9/6 = -2/3 …(i)By section formula,y = (my_{2}+ny_{1})/(m+n)1 = (m×-2+n×p)/(m+n)1 = (-2m+pn)/(m+n)m+n = -2m+pn3m = (p-1)nm/n = (p-1)/3 ….(ii)Equating (i) and (ii)(p-1)/3 = -2/3p-1 = -2p = -2+1 = -1Hence the value of p is -1.