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Question

Find the value of a for which the following points A(a,3),B(2,1) and C(5,a) are collinear. Hence find the equation of the line.

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Solution

Given: A(a,3),B(2,1) and C(5,a) are collinear.
Slope of AB= Slope of BC
132a=a152
22a=a13
6=(2a)(a1)
6=2a2a2+a
a23a4=0
a24a+a4=0
(a4)(a+1)=0
a=4,1
For a=4
Slope of BC=a152=413=33=1
Equation of BC;(y1)=1(x2)
y1=x2
xy=1

For a=1
Slope of BC=a152=113=23
Equation of BC:(y1)=23(x2)3y3=42x
2x+3y=7

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