Question

A line intersects the $y$-axis and $x$-axis at points $P$ and $Q$ respectively. If the mid point of$PQ$ is $(2,-5)$, then the coordinates of $P$ and $Q$ are:

• A. $(0,-5)and(2,0)$
• B. $(0,10)and(-4,0)$
• C. $(0,4)and(-10,0)$
• D. $(0,–10)and(4,0)$

Answer 1

The correct option is D

$(0,–10)and(4,0)$

Explanation for the correct option:

Option (D) $(0,–10)and(4,0)$

Let the coordinates of $P$ be $(0,y)$ and $Q$ be$(x,0)$

Midpoint of $PQ$ $=(2,-5)$

By midpoint formula,

$\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)=\left(2,-5\right)$

$$\begin{gathered} \Rightarrow \left(\frac{0+x}{2},\frac{y+0}{2}\right)=(2,-5) \\ \Rightarrow \left(\frac{x}{2},\frac{y}{2}\right)=\left(2,-5\right) \\ \Rightarrow \frac{x}{2}=2and\frac{y}{2}=-5 \\ \Rightarrow x=4andy=-10 \end{gathered}$$

Therefore, the co-ordinates of $P$ and $Q$ are $(0,-10)$ and $(4,0)$respectively.

Hence, Option (D) $(0,–10)and(4,0)$ is the correct option.