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Just Opposite

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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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Find the vertices of a pentagon given the midpoints of its sides.

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.