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 the coordinates of P and Q, respectively, are

(a) (0, −5) and (2, 0)
(b) (0, −10) and (4, 0)
(c) (0, 10) and (−4, 0)
(d) (0, 4) and (−10, 0)

Answer 1

(b) (0, −10) and (4, 0)
Let the line PQ intersect y axis at P(0, a) and x axis at Q(b, 0).
$\text{Midpoint of}PQ=\left(\frac{0+b}{2},\frac{a+0}{2}\right)$
But the midpoint of PQ is (2, −5).
Therefore,
$$\begin{gathered} \frac{0+b}{2}=2\text{and}\frac{a+0}{2}=-5 \\ \Rightarrow b=4\text{and}a=-10. \end{gathered}$$
Therefore,
$$\begin{gathered} P\left(0,a\right)\Rightarrow P\left(0,-10\right) \\ Q\left(b,0\right)\Rightarrow Q\left(4,0\right) \end{gathered}$$
Hence, the coordinates of P and Q are (0, −10) and (4, 0).