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Just Opposite

A and C are the opposite vertices of a square ABCD, and have coordinates (a,b) and (c,d), respectively. What are the coordinates of the vertices B and D? What is the area of the square?

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Ladder and Cube

A 1 metre cube has one face on the ground and one face against a wall. A 4 metre ladder leans against the wall and just touches the cube. How high is the top of the ladder above the ground?

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Is there a relationship between the coordinates of the endpoints of a line and the number of grid squares it crosses?

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.