Copyright © University of Cambridge. All rights reserved.
'At Right Angles' printed from http://nrich.maths.org/
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
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) 