Question

if the point a(1 - 2)b(2 3) c(a 2)d(-4 -3) from a parallelogram, find value of a and height of the parallelogram taking ab as the base

Answer 1

concept: diagonal of parallelogram bisect each other
Therefore,
midpoint of AC =midpoint of BD
$\frac{1 + a}{2} \: \frac{ - 2 + 2}{2} = \frac{2 - 4}{2} \: \frac{3 - 3}{2 } \\ \frac{1 + a}{2} \: \: 0 = \frac{ - 2}{2} \: \: 0$
1+a/2= -2/2( cancel both denominator)
1+a=-2
a=-2-1
a= -3