Two Points not allowed to have same position
When you move the points it is not allowed that both points have a distance of less than 1 in x or y direction. So the sum of their distances along the x-Axis and y-Axis must be at least 1. In more mathematical words you could say that their distance (Taxicab distance) must be at least 1. In addition the points' movements are restricted to the grid.
How to achieve this in GeoGebra
- Create arbitrary points and .
- Make a space around point that is allowed for the other point to be in. This space is the whole plane except a 2 by 2 square around . Set visible in the applet above to visualize it. Make this space by a union of one space that has a distance of at least 1 in x direction ( in the applet above) and another with a distance of at least 1 in y direction ( in the applet above).
- Like step 2 but with point . In the applet above you can see the spaces in , and .
- Create point with the command
PointIn(c). As a result point can not come too close to point . - Create point with the command
PointIn(f). This way can not come too close to point . - Set points and invisible.
- In of point add the line
B=CopyFreeObject(C). This way the space around point , which is the constraint for to move in, moves together with point . - In of point add the line
A=CopyFreeObject(D).