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Q.

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

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a

(0, 0)

b

(0, 2)

c

(- 2, 0)

d

(2, 0)

answer is A.

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Detailed Solution

It is given two points

A (2, 5)

and

B (- 2, - 5)

.
We know that perpendicular bisector of any line segment divides the line segment into two equal parts.
i.e, perpendicular bisector of any line segment always passes through the midpoint of the line segment.
Let the mid point of the line segment joining the points

(2, 5)

and

(- 2, - 5)

is

(x_{1}, y_{1})

.
We know that if a point

C (x, y)

divides the line segment

AB

joining the points

A (x_{1}, y_{1}) B (x_{2}, y_{2})

in the ratio

m : n

.
Then we have,

x = \frac{n x_{1} + m x_{2}}{m + n}

and

y = \frac{n y_{1} + m y_{2}}{m + n}

.
For any midpoint of a line segment m:n = 1:1.
Now putting the values we get,
(

x_{1}, y_{1})

= (\frac{2 + (- 2)}{2}, \frac{5 + (- 5)}{2})

= (\frac{2 - 2}{2}, \frac{5 - 5}{2})

= (

\frac{0}{2}

,

\frac{0}{2})

= (0, 0)

(0, 0)

lies on the perpendicular bisector of

(2, 5)

and

(- 2, - 5)

.
So the correct option is 1.

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