A line intersects $\displaystyle y$-axis and $\displaystyle x$-axis at point P and Q , respectively. If $\displaystyle \mathrm{R}(2,5)$ is the mid-point of line segment PQ , then find the coordinates of P and Q .

Let the coordinates of P and Q be ($\displaystyle 0$, y) and ( \(\displaystyle \mathrm{x}, 0\) ) respectively. \[\begin{aligned} & \because \mathrm{R}(2,5) \text { is the midpoint of } \mathrm{PQ} \\ & \frac{0+\mathrm{x}}{2}=2 \text { and } \frac{y+0}{2}=5 \\ & \therefore \mathrm{x}=4, \mathrm{y}=10 \\ & \mathrm{P}(0,10) \text { and } \mathrm{Q}(4,0) \end{aligned} \]