Question

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

Answer 1

Let the co-ordiantes of $P$ be $(x,y)$ and $Q$ be $(x_2,y_2)$

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

By midpoint formula,

$x=\frac{x_1+x_2}{2}$ and $y=\frac{y_1+y_2}{2}$

$2=\frac{x_1+x_2}{2}$ and $-5=\frac{y_1+y_2}{2}$

$\therefore x_1+x_2=4$ and $y_1+y_2=-10$

Since line $PQ$ intersects the y-axis at $P$

So, $x_1=0$.

Similarly, $y_2=0$

$\therefore x_2=4$ and $y_1=-10$

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