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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 (x1,y1).
We know that if a point C(x,y) divides the line segment AB joining the points Ax1,y1  B(x2,y2) in the ratio m:n.
Then we have,
 x=nx1+mx2m+n and  y=ny1+my2m+n.
For any midpoint of a line segment m:n = 1:1.
Now putting the values we get,
( x1,y1) =(2+(-2)2,5+(-5)2)
=(2-22,5-52)
= (02,02)
 =(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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