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A Tilted Square

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3
Why do this problem?
The problem gives (a,b) and (c,d) as the opposite vertices of a square and asks for the coordinates of the other two vertices. An interactivity leads learners through a succession of tasks so that they construct several squares for themselves that are 'tilted' (i.e.edges not parallel to the axes) and explore the reasons that the shapes they have drawn are actually squares.