Question

The points A(1.-2). B(2.3), C (K2) and D(-4,-3) are the vertices of a parallelogram. Find
the value of k.​

Answer 1

Step-by-step explanation:

Given Points are A(1,2).B(2,3),C(K2)and D(-4,-3).

As we know that diagonals of a parallelogram bisect each other.

Mid point of AC:-

Here

,(x1+y1)=(1,-2)and(x2,y2)=(k,2).

==>[(x1+x2)/2,y1+y2)/2]

==>[(1+k)/2,(-2+2)/2]

==>[(1+k)/2] ......eq.i

Mid point of BD:-

Here,(x1+y1)=(2,3) and (x2,y2). =(-4,-3)

==>[x1+x2)/2,y1+y2)/2]

==>[(2-4)/2,(3-3)/2]

==>[1,0] ....... eq.ii

Comparing eq.i and ii.

==>(1+k)/2=-1

==>1+k=-2

==>k=-3

Therefore the value of k=-3