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Deepak Bora
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Three vertices of a parallelogram ABCD taken in order are A (3, 6), B (5, 10) and C (3, 2) find: (i) the coordinates of the fourth vertex D. (ii) length of diagonal BD. (iii) equation of side AB of the parallelogram ABCD.

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An Important Question of class 10 Based on Equation of a Straight Line Chapter of M.L Aggarwal for ICSE BOARD.
Here three vertices of a parallelogram is given
So, you have to find the coordinates of the fourth vertex , length of diagonal and equation of a side.
This is the Question Number 29, Exercise 12.1 of M.L Aggarwal.

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  1. Given, the three vertices of a parallelogram ABCD taken in order are A (3, 6), B (5, 10) and C (3, 2)

    (i) We know that the diagonals of a parallelogram bisect each other.

    Let (x, y) be the co-ordinates of D

    Hence, we have

    Mid-point of diagonal AC = ((3 + 3)/2, (6 + 2)/2) = (3, 4)

    Mid-point of diagonal BD = ((5 + x)/2, (10 + y)/2)

    ML Aggarwal Solutions for Class 10 Chapter 12 - 7And, these two should be the same

    On equating we get,

    (5 + x)/2 = 3 and (10 + y)/2 = 4

    5 + x = 6 and 10 + y = 8

    x = 1 and y = -2

    Thus, the co-ordinates of D = (1, -2)

    (ii) Length of diagonal BD

    ML Aggarwal Solutions for Class 10 Chapter 12 - 8

    (iii) Equation of the side joining A (3, 6) and D (1, -2) is given by

    ML Aggarwal Solutions for Class 10 Chapter 12 - 9

    4 (x – 3) = y – 6

    4x – 12 = y – 6

    4x – y = 6

    Thus, the equation of the side joining A (3, 6) and D (1, -2) is 4x – y = 6.

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