Question

ABCD is a parallelogram. If A(3,-4), C(-6,5), D(-2,1) then find the coordinate of point B​

Answer 1

Let A(1,−2), B(3,6) and C(5,10) be the three vertices of a parallelogram ABCD and let its fourth vertex be D(a,b). 

Join AC and BD. Let AC and BD intersect at point O. 

We know that the diagonals of a parallelogram bisect each other. 

So, O is the midpoint of AC as well as that of BD.

Using Midpoint formula X=(2x1+x2)and Y=(2y1+y2)

A(1,−2)≡(x1,y1), C(5,10)≡(x2,y2) 

Midpoint of AC is (21+5,2−2+10), i.e.,(3,4)

Midpoint of BD is (23+a,26+b)

∴ 23+a=3 and 26+b=4

3+a=6 and 6+b=8

a=3 and b=2

Hence, the fourth vertex is D(3,2)

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