Q157 / 270 · NDA 2016 (Phase 1) · Mathematics
A straight line intersects x and y yxes at P and Q respectively. If $(3,5)$ is the middle point of $P Q$, then what is the area of thetriangle OPQ?
- A12 square units
- B15 square units
- C20 square units
- Correct answerD30 square units
Solution
As we know that line $P Q$ intersects $x$-axis and $y$-axis at $P$ and $Q$.
$\because \mathrm{M}$ is the mid point of PQ $\begin{aligned} \therefore & \frac{x+0}{2}=3 \text { and } \frac{0+y}{2}=5 \\ & \Rightarrow x=6 \text { and } y=10 \end{aligned}$ Hence area of triangle $O P Q=\frac{1}{2} \times 6 \times 10=30$ sq. unit
$\because \mathrm{M}$ is the mid point of PQ $\begin{aligned} \therefore & \frac{x+0}{2}=3 \text { and } \frac{0+y}{2}=5 \\ & \Rightarrow x=6 \text { and } y=10 \end{aligned}$ Hence area of triangle $O P Q=\frac{1}{2} \times 6 \times 10=30$ sq. unit
Hence, the correct answer is option: 'D'.