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Question

The mid-points of the sides BC,CA and AB of ABC are D(2,1),E(1,3) and P(4,0) respectively. Find the co-ordinates of A,B and C.

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Solution

Let A(x1,y1) ; B(x2,y2) ; C(x3,y3)
So, x1+x22=4 and y1+y22=0
x2+x32=2 and y2+y32=1
x3+x12=1 and y1+y32=3
On solving equations in x1,x2,x3 and y1,y2,y3, we get x1=1, x2=7, x3=3 and y1=4, y2=4, y3=2
So, A(1,4) ; B(7,4) ; C(3,2)

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