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Question

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

a) (0,0)      b) (0,2)     c) (2,0)    d) (-2,0)


Solution

Given points are $A\left(-2,\: -5\right)\: \text{and}\: B\left(2,\:5\right)$,

Perpendicular bisector of the line joining $AB$ is the line which passed through its mid point and is perpendicular to it.

Mid point of a line joining the points $\left(x_1,\:y_1\right)\:\text{and}\:\left(x_2,\:y_2\right)$ is given by $\left(\frac{x_1+x_2}{2},\:\frac{y_1+y_2}{2}\right)$ 

So midpoint of $AB$ will be $\left(\frac{-2+2}{2},\:\frac{-5+5}{2}\right)=\left(0,\:0\right)$ 

That is the point $\left(0,\:0\right)$ lies on the perpendicular bisector of line segment joining the points $A\left(-2,\: -5\right)\: \text{and}\: B\left(2,\:5\right)$

Therefore option A is correct.

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