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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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Pentagon

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

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Beelines

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

Ladder and Cube

Stage: 4 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

A cube (1 metre by 1 metre by 1 metre) has one face on the ground and one face pressed up to a wall. A ladder, 4 metres long, is leaning against the wall and it just touches the cube. How high is the top of the ladder above the ground?