Question

the points a(1 -2) b(2 3) c(k 2) and d(-4 -3) are the vertices of a parallelogram. Find the value of k.

Answer 1

As we know diagonals of parallelogram bisect each other

So mid point of AC=mid point of BD

A( 1,-2)

C( K,2)

MID point = (1+k)/2, ( -2+2)/2 = 1+k)/2 , 0

B ( 2,3)

D ( -4,-3)

mid point of BD = ( 2 -4)/2, (3-3)/2 = -2/2,0 = -1,0

Comparing x coordinate

(1+k)/2 = -1

1+k = -2

k= -2 -1 = -3

Answer 2

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