Part of a toy is made of two rectangular blocks that are both 4 cm by 8 cm. One of the blocks turns about the other by a hinge, H, that is in the corner of each block.
The top block, ABCH, turns clockwise through a quarter turn.
What shape does A trace out as the block turns?
Where does A end up?
Solution
A is always the same distance from H. So A traces out a quarter circle with radius the length of AH (which is 8 cm).
After the block has turned, AH lies along HQ, so A is on top of the point Q.
Extension
What shape does B trace out and where does it end up?