Question

All the points equidistant from two given points A and B lie on the __ of the line segment AB​

Answer 1

All the points equidistant from two given points A and B lie on the perpendicular bisector of the line segment AB.

Step-by-step explanation:

All the points equidistant from two given points A and B lie on the perpendicular bisector of the line segment AB.

See the attached diagram.

We see that C is the midpoint of the line segment AB and so, AC = BC.

Now, we draw a perpendicular line to AB at C which is DE and hence it is the perpendicular bisector of the line segment AB.

Here, any point on DE (say D or E) is equidistant from A and B both

So, AD = BD and AE = BE. (Answer)