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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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