Equidistant to Points
- mr. fay
The set of equidistant points to a set S are the points that have equal distance to each element in the set S.
Example: Vertices of a Pentagon
1. Draw all the points 4 units from the given point.
2. What is the set of all equidistant points to a given point? ( hint consider all distances )
3. Draw 4 points equidistant to the two given points.
4. What is the set of all equidistant points to the set of two distinct point?
5. Prove the segments XA and XB are congruent. Recall corresponding parts of congruent triangles are congruent.
This implies that any point on the perpendicular bisector of 2 points is equidistant to those 2 points. But are they the only points?
6. Prove the angles YMA and BMY are congruent and therefore 90 degrees.
Therefore the point Y is on the perpendicular bisector.