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If two vertices of a parallelogram are (3, 2) ( – 1, 0) and its diagonals meet at (2, – 5), find the other two vertices of the parallelogram.

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ICSE Board Question Based on Section Formula Chapter of M.L Aggarwal for class10
In this question given that if two vertices of a parallelogram are (3, 2) ( – 1, 0) and its diagonals meet at (2, – 5), find the other two vertices of the parallelogram.
This is the Question Number 25, Exercise 11 of M.L Aggarwal.

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  1. Let A(3,2) and B(-1,0) be the two vertices of the parallelogram ABCD.

    Let M(2,-5) be the point where diagonals meet.

    Since the diagonals of the parallelogram bisect each other, M is the midpoint of AC and BD.

    Consider A-M-C

    Let co-ordinate of C be (x2,y2)

    x1 = 3, y1 = 2

    x = 2, y = -5

    By midpoint formula, x = (x1+x2)/2

    2 = (3+x2)/2

    3+x2 = 4

    x2 = 4-3 = 1

    By midpoint formula, y = (x1+x2)/2

    -5 = (2+y2)/2

    -10 = 2+y2

    y2 = -10-2 = -12

    Hence the co-ordinates of the point C are (1,-12).

    Consider B-M-D

    Let co-ordinate of D be (x2,y2)

    x1 = -1, y1 = 0

    x = 2, y = -5

    By midpoint formula, x = (x1+x2)/2

    2 = (-1+x2)/2

    -1+x2 = 4

    x2 = 4+1 = 5

    By midpoint formula, y = (x1+x2)/2

    -5 = (0+y2)/2

    -10 = 0+y2

    y2 = -10

    Hence the co-ordinates of the point D are (5,-10).

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