M.L Aggarwal book Important Question of class 10 chapter Based on Equation of a Straight Line for ICSE BOARD.
Here some points are given that are collinear
A (a, 3), B (2,1) and C (5, a)
You have to find the value of a and the equation of the line.
This is the Question Number 20 Exercise 12.1 of M.L Aggarwal.
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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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Given,
Points A (a, 3), B (2,1) and C (5, a) are collinear.
So, slope of AB = slope of BC
⇒ -6 = (a – 1) (2 – a) [On cross multiplying]
-6 = 2a – 2 – a2 + a
-6 = 3a – a2 – 2
a2 – 3a – 4 = 0
a2 – 4a + a – 4 = 0
a (a – 4) + (a – 4) = 0
(a + 1) (a – 4) = 0
a = -1 or 4
As a = -1 doesn’t satisfy the equation
⇒ a = 4
Now,
Slope of BC = (a – 1)/(5 – 2) = (4 – 1)/3 = 3/3 = 1 = m
So, the equation of BC is
(y – 1) = 1 (x – 2)
y – 1 = x – 2
x – y = -1 + 2
Thus, the equation of BC is x – y = 1.