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This problem offers a good opportunity for students to discuss images 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.
This printable worksheet may be useful: Route To Infinity
You may be interested in our collection Dotty Grids - an Opportunity for Exploration, which offers a variety of starting points that can lead to geometric insights.
Before working on this problem, spend time on Cops and Robbers and Coordinate Patterns to develop students' fluency with coordinates.