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Deepak Bora
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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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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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1 Answer

  1. Given,

    Points A (a, 3), B (2,1) and C (5, a) are collinear.

    So, slope of AB = slope of BC

    ML Aggarwal Solutions for Class 10 Chapter 12 - 2

    ⇒ -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.

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