Question

If the points A(6, 1), B(8, 2), C(9, 4) and D(p, 3) are the vertices of a parallelogram, taken inorder, find the value of p

Answer 1

Solution : We know that diagonals of parallelogram bisect each other.
So, the coordinates of the midpoint of $AC=$ Coordinates of the midpoint of $BD$.
i.e., $(\frac{6+9}{2},\frac{1+4}{2})=(\frac{8+p}{2},\frac{5}{2})$
$$\begin{array}{cc}& (\frac{15}{2},\frac{5}{2})=(\frac{8+p}{2},\frac{5}{2})\\ & \frac{15}{2}=\frac{8+p}{2}\\ & 15=8+p\Rightarrow p=7\end{array}$$