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

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(1,2)

(0,0)

(1,2)

(1,3)

answer is B.

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Detailed Solution

Given points are

A (- 2, - 5) and B (2, 5)

.
We have to find out the point which lies on the perpendicular bisector of the line segment joining the points

A (- 2, - 5) and B (2, 5)

.
Let the perpendicular bisector of the line segment goes through the point

(x, y)

.
We know that, the perpendicular bisects of the line always pass through the mid-point of the line segment, so we can say that

(x, y)

will be the mid-point of points

A (- 2, - 5)

and

B (2, 5)

.
Now,
We know that if the coordinates of two points are

x 1, y 1

and

x 2, y 2

then coordinate of the midpoint of the two points will be

x 1 + x 2 2, y 1 + y 2 2

.
Then, the coordinates of the point lie on the perpendicular bisects on the line segment joining the points

A (- 2, - 5) and B (2, 5)

(x, y) = − 2 + 2 2, − 5 + 5 2 ⇒ (x, y) = (0, 0)

∴

The point is (0,0).
Hence, option (2) is correct.

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