Two Points Plus One Line
Age 14 to 16
This problem gives an opportunity to find the parameters that
express the generality in the context.
For example, if the distance between the feet of perpendiculars
dropped from $A$ and $B$ is taken as the unit length, then the
length of the perpendiculars can be expressed in terms of that
There may be other useful unit lengths to consider, but the
important skill is to see that enlarging the diagram doesn't change
the feature being explored, so a thoughtful choice of unit can help
to make the problem more convenient to handle and access.