Question

If the 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

Consider the given points be

$A(6,1),B(8,2),C(9,4)$ and $D(p,3)$

Let $AC$ and $BD$ be two diagonals bisect each other.

Let $O$ be the mid point of $AC$ and $BD$.

Now, first we find that mid point of $AC$$(X-ordinates)$

$x=\frac{6+9}{2}=\frac{15}{2}$ …….. (1)

Now, we find that mid point of $BD$$(X-ordinates)$

$x=\frac{8+p}{2}$ ……… (2)

By equation (1) and (2) to we get,

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

$8+p=15$

$p=15-8=7$

$p=7$

Hence it is complete solution.