# A line intersects the y-axis and x-axis at the points P and Q respectively. If (2, –5)

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.