the idea for this work comes from the very fine NRICH Diamond Collector task

in which students try to create straight lines that collect as many diamonds as possible:

there are three levels - increasingly complex

the idea of the tasks below is that students try to find three straight lines

(none of which are vertical or horizontal)

passing through the 9 points

on each of the 3 lines, find a missing 4th coordinate pair to create 4-in-a-line

then find the equations of the 3 lines

(in the example there is more than one option; I hope that in the questions the three lines should each have 3 coordinates on them)

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