NRICH: At Right Angles

Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?

This problem follows on from How Steep is the Slope?

It’s easy to draw parallel lines – just check that the gradients match.

 

 

Gradient 32 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  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?

Age 14 to 16


Algebra & Pre-Algebra, Functions & Graphs
High School, Educator

What are you looking for?

Organization

NRICH (University of Cambridge)

Website URL

Type of Resource

Challenge

Assigned Categories