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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. 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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