# Locus (A)

- Author:
- Roger Gemberling

In the first sketch, point Y is exactly 2 units from point X. Move points A, B, C, ... , and J so each point is 2 units from point X. Place all of the points before checking your distances.
Click on each

*to check your estimated distances from point X. How close did you get? Use the GeoGebra tools to construct the path (or paths) ALL of the points that have a distance of 2 units from point X.***Button**In the second sketch, point Y is 3 units from the given line. The 3 units is the

*to the line. Move points A, B, C, ... , and J so each point has a shortest distance of 3 units to the line. Place all of the points before checking your distances. Click on each***shortest path***to check your estimated distances. How close did you get? Use the GeoGebra tools to construct the path (or paths) for ALL of the points that have a***Button****shortest path**distance of 3 units from the line.In the final sketch, move each point (A, B, C, ... , and J) so the point has the same distance to points X and Y. Place all of the points before checking your distances.

*: If the distance from A to X is 3.7, then the distance from A to Y is also 3.7. If the distance from B to X is 4.9, then the distance from B to Y is also 4.9. Click on each***Examples***to check your estimated distances. Use the GeoGebra tools to construct the path (or paths).***Button**