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.
Solution:
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
$\left(\frac{x+0}{2}, \frac{0+y}{2}\right)=(2,-5)$
$\Rightarrow\left(\frac{x}{2}, \frac{y}{2}\right)=(2,-5)$
$\Rightarrow \frac{x}{2}=2$ and $\frac{y}{2}=-5$
$\Rightarrow x=4, y=-10$
Thus, the coordinates of P and Q are (0, −10) and (4, 0), respectively.