Question

The set of all points in a plane that are equidistant from two points is an

Answer 1

A midpoint.

It is a set of points (single point) that is equidistant from point A and point B.

In other words the distance between point A and midpoint M is equal to the distance between point M and point B.

Answer 2

The set of all points in a plane that are equidistant from two points is a Perpendicular Bisector.

Explanation:

Given: Two points on the plane.

We need to find what has set of all such point which is equidistant from two given fixed point.

Point which is equidistant from two fixed point is known as mid point of the line segment formed by joining the fixed points.

So, all the point which is equidistant from fixed points form a perpendicular bisector.

Therefore, The set of all points in a plane that are equidistant from two points is a Perpendicular Bisector.