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

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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?

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 pushed up against a wall.

A 4 metre long ladder is leaning against the wall, just touching the cube.

How high is the top of the ladder above the ground?