# Equidistant: Definition & Formula

Instructor: Beverly Maitland-Frett

Beverly has taught mathematics at the high school level and has a doctorate in teaching and learning.

This lesson will discuss the concepts of equidistant and midpoint. We will explore the midpoint formula and show some examples of relevance in the real world setting.

## Definition of Equidistant

In soccer, the midfielder is a highly regarded position. If you are a soccer fan, you will agree that this player is posted somewhere around the middle of the field, not at either goals. Likewise in American football, the midfield is an important position on the field. Equidistant, in concept, may be associated with these players and positions, in that they all have to do with the middle. Equidistant comes from two words, equal and distant. An equidistant point is a point that is an equal distance from two other points. Please note, an equidistant point is not necessarily in the middle of two points. For example, you may live near two Walmart locations that are both 6.5 miles away from you. However, your house is not necessarily located between the two Walmart locations.

Therefore, any point that is equidistant may be a midpoint or it may also be points that lie on the perpendicular bisector of a line segment. Line segment RS as shown below, is the perpendicular bisector of line segment PQ.

Remember that the perpendicular bisector is the line or line segment that cuts another line in half, simultaneously forming a right angle. Look at the diagram below, since points R, O, N, M, T, S all lie on the perpendicular bisector, they are equidistant from points P and Q. However, only point M is the midpoint of line PQ.

## Midpoint Formula

If a pilot, sailor or a voyager wants to know about location and distances, they will use a map to investigate distances. Maps provide exact location and coordinates of places. Sometimes we look at maps and guess how far away a place is with respect to our present location. In order to find a point that is equidistant from other points, we can use the midpoint formula, once we know the x and y coordinates.

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