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Deepak Bora
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Three consecutive vertices of a parallelogram ABCD are A (1, 2), B (1, 0) and C (4, 0). Find the fourth vertex D.

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This question is Based on Section Formula Chapter of M.L Aggarwal book for ICSE BOARD for class 10.
Here three consecutive vertices of a parallelogram ABCD are given. Find the fourth vertex D.
This is the Question Number 23, Exercise 11 of M.L Aggarwal.

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1 Answer

  1. Let M be the midpoint of the diagonals of the parallelogram ABCD.

    Co-ordinate of M will be the midpoint of diagonal AC.

    Given points are A(1,2), B(1,0) and C(4,0).

    Consider line AC.

    x= 1, y1 = 2

    x= 4, y2 = 0

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

    x = (1+4)/2 = 5/2

    By midpoint formula, y = (y1+y2)/2

    y = (2+0)/2 = 2/2 = 1

    Hence the co-ordinates of M are (5/2,1).

    M is also the midpoint of diagonal BD.

    Consider line BD and M as midpoint.

    x= 1, y1 = 0

    x = 5/2, y = 1

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

    5/2 = (1+x2)/2

    5 = 1+x2

    x2 = 5-1 = 4

    By midpoint formula, y = (y1+y2)/2

    1 = (0+y2)/2

    1 = y2/2

    y2 = 2

    Hence the co-ordinates of D are (4,2).

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