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Deepak Bora
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ABCD is a rhombus. The co-ordinates of A and C are (3, 6) and ( – 1, 2) respectively. Write down the equation of BD.

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ICSE Board Question Based on Equation of a Straight Line Chapter of M.L Aggarwal for class10
In this question two co-ordiantes of a rhombus is given. Solve this question
This is the Question Number 37, Exercise 12.2 of M.L Aggarwal.

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  1. Given, ABCD is a rhombus and co-ordinates of A are (3, 6) and of C are (-1, 2)

    Slope of AC (m1) = (2 – 6)/ (-1 – 3) = -4/-4 = 1

    We know that, the diagonals of a rhombus bisect each other at right angles.

    So, the diagonal BD is perpendicular to diagonal AC

    Let the slope of BD be m2

    Then, m1 x m2 = -1

    m2 = -1/(m1)

    = -1/ (1) = -1

    Now, the co-ordinates of the mid-point of AC is given by

    ((3 – 1)/2, (6 + 2)/2) = (2/2, 8/2) = (1, 4)

    So, the equation of BD will be

    y – 4 = -1 (x – 1)

    y – 4 = -x + 1

    x + y = 5

    Thus, the equation of BD is x + y = 5.

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