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Deepak Bora
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The line through A (– 2, 3) and B (4, b) is perpendicular to the line 2x – 4y = 5. Find the value of b.

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This is the Important question of class 10 Based on Equation of a Straight Line Chapter of M.L Aggarwal book for ICSE BOARD.
Here the line through given coordinates is perpendicular to a line.
So, fnd the solution
This is the Question Number 09, Exercise 12.2 of M.L Aggarwal.

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  1. The slope of the line passing through A (-2, 3) and B (4, b) will be

    m1 = (b – 3)/ (4 + 2) = (b – 3)/ 6

    Now, the gradient of the given line 2x – 4y = 5 is

    4y = 2x + 5

    y = (2/4) x + 5/4

    y = ½ x + 5/4

    So, m2 = ½

    As the line are perpendicular to each other, we have

    m1 x m2 = -1

    (b – 3)/ 6 × ½ = -1

    (b – 3)/ 12 = -1

    b – 3 = -12

    b = -12 + 3 = -9

    Hence, the value of b is -9.

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