Question

A line intersects the y-axis and x-axis at the points P and Q respectively. If (2, –5) is the midpoint of PQ then find the coordinates of P and Q. [CBSE 2017]

Answer 1

Suppose the line intersects the y-axis at P(0, y) and the x-axis at Q(x, 0).

It is given that (2, –5) is the mid-point of PQ.

Using mid-point formula, we have
$$\begin{gathered} \left(\frac{x+0}{2},\frac{0+y}{2}\right)=\left(2,-5\right) \\ \Rightarrow \left(\frac{x}{2},\frac{y}{2}\right)=\left(2,-5\right) \\ \Rightarrow \frac{x}{2}=2\mathrm{and}\frac{y}{2}=-5 \\ \Rightarrow x=4,y=-10 \end{gathered}$$
Thus, the coordinates of P and Q are (0, −10) and (4, 0), respectively.