Question

P(–3, 2) is the mid-point of line segment AB as shown in the given figure. Find the co-ordinates of points A and B.

Answer 1

Point A lies on y-axis, so let its co-ordinates be (0, y).

Point B lies on x-axis, so let its co-ordinates be (x, 0).

P(–3, 2) is the mid-point of line segment AB.

∴ ${\displaystyle (-3,2)=(\frac{0+x}{2},\frac{y+0}{2})}$

${\displaystyle \Rightarrow (-3,2)=(\frac{x}{2},\frac{y}{2})}$

${\displaystyle \Rightarrow -3=\frac{x}{2}}$ and ${\displaystyle 2=\frac{y}{2}}$

${\displaystyle \Rightarrow }$ −6 = x and 4 = y

Thus, the co-ordinates of points A and B are (0, 4) and (−6, 0) respectively.