Question

Points $A(6,1),B(8,2),C(9,4)$ and $D(p,3)$ are the vertices of a parallelogram, taken in order. Find the value of $p$.

Answer 1

We know that diagonal of parallelogram bisect each other

So, $O$ is the mid-point of $AC$ & $BD$

Finding mid point of $AC$

We know to find x co-ordinate of $O$

x-coordinate of $O$ $=\frac{x_1+x_2}{2}$

where $x_1=6,x_2=9$

$=\frac{6+9}{2}$

$=\frac{15}{2}.........\left(1\right)$

Finding mid point of $BD$

We know to find x co-ordinate of O

x-coordinate of $O$ $=\frac{x_1+x_2}{2}$

where $x_1=8,x_2=p$

$=\frac{8+p}{2}.........\left(2\right)$

Comparing (1) and (2). we get

$\frac{15}{2}=\frac{8+p}{2}$

$15=8+p$

$p=7$