Question

Given $O(0,0),P(1,2),S(-3,0)$. $P$ divides $OQ$ in the ratio $2:3$ and $OPRS$ is a parallelogram. Find the coordinates of $Q$

Answer 1

Let the coordinates of point $Q$ be $(h,k).$

$P$ divides $OQ$ in the ratio $2:3$.

Now, by using section formula coordinates of point $P$ will be,

$(\frac{2h+3\left(0\right)}{2+3},\frac{2k+3\left(0\right)}{2+3})=(\frac{2h}{5},\frac{2k}{5})$

But coordinates of point $P$ are $(1,2)$. Therefore,

$\Rightarrow \frac{2h}{5}=1\text{and}\frac{2k}{5}=2$

$\Rightarrow 2h=5\text{and}k=5$

$\Rightarrow h=2.5\text{and}k=5$

Hence, coordinates of point $P$ are $(2.5,5).$