A, B and C do not lie in a straight line. How could you tell without
drawing?
It looks as though D, E and F do lie in a straight line. How can
you be sure?
Can you find 3 other points which look as though they lie on a line
but do not?
© MEI 2009
Teachers’ notes
• This could fit in with equations of straight line
graphs, gradient or vectors.
• There are at least 3 ways of deciding whether 3
points lie in a line without drawing:
– Gradient (see later)
– Vectors (see later)
– Equation of straight line
• Drawing can be misleading if the points are very
close to being in a line. This is the idea behind
the puzzle on the next page.
© MEI 2009
Missing area puzzle
© MEI 2009
Using gradient
3
− = −0.6
5
4
− = −0.5
8
Gradient of AB is
. Gradient of BC is
The gradients are different so ABC is not a straight line.
Gradient of DE is
5
2
=1
3
3
Gradient of EF is
10 5
2
= =1
6 3
3
The gradients are
the same so DEF
is a straight line.
© MEI 2009
Using vectors
JJJG ⎛ 8 ⎞
JJJG ⎛ 13 ⎞
AB = ⎜ ⎟
AC = ⎜ ⎟
−
4
⎝ ⎠
⎝ −7 ⎠
.
Neither vector cannot be written as a multiple of the other so ABC is not a straight line.
JJJG ⎛ 3 ⎞
DE = ⎜ ⎟
⎝ 5⎠
JJJG ⎛ 9 ⎞
DF = ⎜ ⎟
⎝ 15 ⎠
JJJG JJJG
DF = 3DE
DEF is a
straight line.
© MEI 2009