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This problem offers a good opportunity for students to discuss patterns and find convincing arguments for their solutions.
Reuben Hersh has written that:
"In the classroom, convincing is no problem. Students are too easily convinced. Two special cases will do it."
This problem offers an opportunity to ensure that students are justified in generalising from the particular cases that they have selected.
Before working on this problem students could develop fluency in using coordinates by working on Cops and Robbers and fluency with linear sequences by taking a look at Shifting Times Tables.
Find a general symbolic expression for the coordinates of the vertices of the $n$th square or triangle.