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

Something in Common

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

You might also like to look at the problem called "Tilted Squares" published in Sept04.

Some cubes or a construction set might help you to visualise a 3D grid.

How many points are there that are $ \surd 3$ units from (0,0,0)?