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Question

Find the coordinates of the point where the diagonals of the parallelogram formed by joining the points (−2,−1), (1,0), (4,3) and (1,2) meet.

A
(5,1)
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B
(1,1)
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C
(1,5)
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D
(1,1)
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Solution

The correct option is B (1,1)
Given are the coordinates of the four vertices of a parallelogram.
To find out: The coordinates of the point of intersection of the two diagonals of the parallelogram.

Let the vertices of the parallelogram be A(2,1),B(1,0),C(4,3),D(1,2)
We know that, the diagonals of a parallelogram bisect each other.
Hence, the diagonals AC and BD would meet at the midpoint of AC and BD.
We also know that the coordinates of the midpoint of the line segment joining (x1,y1) and (x2,y2) are:

P(x,y)=(x1+x22,y1+y22)

Hence, mid point of AC =(2+42,1+32)=(1,1)

Hence, option B is correct.

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