Lying and Cheating

Follow the instructions and you can take a rectangle, cut it into 4 pieces, discard two small triangles, put together the remaining two pieces and end up with a rectangle the same size. Try it!

Muggles Magic

You can move the 4 pieces of the jigsaw and fit them into both outlines. Explain what has happened to the missing one unit of area.

Walk and Ride

How far have these students walked by the time the teacher's car reaches them after their bus broke down?

At Right Angles

Stage: 3 Challenge Level:

This problem follows on from How Steep is the Slope?

It's easy to draw parallel lines - just check that the gradients match.

 Gradient $\frac{3}{2}$ Gradient $0$ Gradient $-2$

But I'm finding it harder to draw perpendicular lines. Here are my best efforts so far but I don't think they're quite right!

I know that the sides of a square are at right angles, so if I learn to draw tilted squares I may be able to find an efficient method for drawing perpendicular lines.

Experiment with the interactivity below until you can draw squares with confidence.
Work out the gradients of the lines which form your squares.
Is there a relationship between the gradients of perpendicular lines?
Can you use your relationship to explain why the two sets of lines above are not perpendicular?

Full Screen Version
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Here are some pairs of coordinates which can be joined to make straight lines.
Decide whether the two lines are perpendicular or not, and explain how you know.
Can you decide without plotting the points?

 First line Second line Through (6,9) and (10,1) Through (4,2) and (14,7) Through (6,8) and (21,12) Through (1,4) and (5,14) Through (-3,-2) and (-1,1) Through (6,1) and (15,-5)