Question

The point which lies on the perpendicular bisector of the line segment joining the points $A\left(-2,-5\right)$ and $B\left(2,5\right)$ is

• A. $\left(0,0\right)$
• B. $\left(0,2\right)$
• C. $\left(2,0\right)$
• D. $\left(-2,0\right)$

Answer 1

The correct option is A

$\left(0,0\right)$

The perpendicular bisector of a line segment passes through its midpoint.

Let P be the midpoint of line segment joining the points A and B

So, the coordinates of P are given by the formula

$P\left(x,y\right)=\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$

Where $x_1=-2,x_2=2,y_1=-5,y_2=5$

$$\begin{gathered} P\left(x,y\right)=\left(\frac{-2+2}{2},\frac{-5+5}{5}\right) \\ =\left(\frac{0}{2},\frac{0}{2}\right) \\ =(0,0) \end{gathered}$$

Also, the midpoint of A and B i.e., $\left(0,0\right)$ lies on perpendicular bisector of A and B.

Hence, option A is correct.