Question

A (1-2), B (2, 3) C (k. 2) and D(-4,-3) are
the co-ordinates of the vertices
of
parallelogram ABCD Find the value of 'k'​

Answer 1

Diagonals bisects each other in a parallelogram

Therefore,

Midpoint of AC = Midpoint of BD

$\boxed{\large{Midpoint \: = ( \frac{x2 + x1}{2} \: \: , \frac{y2 + y1}{2} )} }$

$\hookrightarrow \mathtt{= ( \frac{k + 1}{2} , \frac{2 - 2}{2} ) =( \frac{ - 4 + 2}{2} } \: , \frac{ - 3 + 3}{2} )$

$\hookrightarrow \dfrac{k + 1}{2} = - 1$

$\hookrightarrow \: k + 1 = - 2 \\ \implies \boxed{ k = - 3}$

__________________________

k = -3

hope it helps...