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Question

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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Solution



We know that by section formula, the co-ordinates of the points which divide internally the line segment joining the points (x1,y1) and (x2,y2) in the ratio m:n is
(x,y)=(mx2+nx1m+n,my2+ny1m+n)
O is the midpoint of AC and BD

(2,5)= mid point of AC

(2,5)=(x1+32,y1+22)

x1+32=2

x1+3=4

x1=1

Also, y1+22=5

y1+2=10

y1=12

c=(1,12)

(2,5)= Mid point of BD

(2,5)=(1+x22,0+y22)

1+x22=2

1+x2=4

x2=5

0+y22=5

y2=10

D=(5,10)

1377943_1228972_ans_f3c8ac6be9a945f3960a1fb6a5cf9284.JPG

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