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Deepak Bora
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The points B (1, 3) and D (6, 8) are two opposite vertices of a square ABCD. Find the equation of the diagonal AC.

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An Important Question of M.L Aggarwal book of class 10 Based on Equation of a Straight Line Chapter for ICSE BOARD.
Co-ordinates of two opposite vertices of a square are given. Find the equation of the diagonal AC.
This is the Question Number 36, Exercise 12.2 of M.L Aggarwal.

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  1. Given, points B (1, 3) and D (6, 8) are two opposite vertices of a square ABCD

    Slope of BD is given by

    m= (8 – 3)/ (6 – 1) = 5/5 = 1

    We know that, the diagonal AC is a perpendicular bisector of diagonal BD

    So, the slope of AC (m2) will be

    m1 x m2 = -1

    1 x m2 = -1

    m2 = -1

    And, the co-ordinates of mid-point of BD and AC will be

    ((1 + 6)/2 , (3 + 8)/2) = (7/2, 11/2)

    So, the equation of AC is

    y – 11/2 = -1 (x – 7/2)

    2y – 11 = -2x – 7

    2x + 2y – 7 – 11 = 0 ⇒ 2x + 2y – 18 = 0

    Thus, the equation of diagonal AC is x + y – 9 = 0.

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