NRICH: At Right Angles
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 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?
| 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) |
Age 14 to 16
What are you looking for?
Organization
Website URL
Type of Resource
Online Interactive Activity
Assigned Categories
Resource k12
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 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?
| 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) |
Age 14 to 16
What are you looking for?
Organization
Website URL
Type of Resource
Online Interactive Activity