Question

If the points $A(6,1),B(8,2),C(9,4)$ & $D(p,3)$ are the vertices of a parallelogram, taken in order, then the value of p is -

• A. $5$
• B. $7$
• C. $9$
• D. $2$

Answer 1

Answer: (B)

$7$

It is given that ABCD is parallelogram.

If the points $A(6,1),B(8,2),C(9,4),D(p,3)$ are the vertices of a parallelogram.

We know that the diagonals of a parallelogram bisect each other.

So, the co-ordinates of the mid-point of $AC=$ the co-ordinates of the mid-point $BD$.

$\Rightarrow$ $(\frac{6+9}{2},\frac{1+4}{2})$ $=(\frac{8+p}{2},\frac{2+3}{2})$

$\Rightarrow$ $(\frac{15}{2},\frac{5}{2})=(\frac{8+p}{2},\frac{5}{2})$

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

$\Rightarrow$ $15=8+p$

$\therefore$ $p=7$