four rectangles

this idea is suggested by David Wells, in his 'Curious and Interesting Geometry' book
on page 169 he indicates that this rule is the dual of Pappus' theorem involving points lines, meets and joins

the four rectangles above have an easily seen answer
but diagrams are not to be relied upon.... and these are 'easy' special cases...

an intention is that students find straight line graph equations for the diagonals; set up and solve equations, pairwise, to establish that there is a common meeting point

or, at least, check that an apparent point of intersection fits the three line equations

students can set up their own examples - they are likely to encounter some hefty fraction calculations (which a calculator can handle if this becomes too demanding or tedious)