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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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Pentagon

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

Working through the interactivity should help you with this. It is also worth going back to the first page of the interactivity and trying out your ideas there.

There are several possible approaches to the final problem:

  1. Using Pythagoras theorem - which is hard work.
  2. Using the fact that the square can be split into 45° right angled triangles and some simple trig.
  3. Some symmetry and the differences in the x and y coordinates of the vertices and the coordinates of the centre of the square.