Graphics Reference
In-Depth Information
Y
X
a
Fig. 12.6.
Two lines intersecting at an angle
α
.
Y
P
3
X
P
2
P
1
Fig. 12.7.
Three points on a common line.
12.8 Test If Three Points Lie On a Straight Line
Three points either create a triangle or lie on a straight line as shown in
Figure 12.7. To determine when this occurs we compare two vectors formed
from the points.
For example, given
P
1
(
x
1
,y
1
)
,P
2
(
x
2
,y
2
)
,P
3
(
x
3
,y
3
)and
r
=
−−→
P
1
P
2
and
s
=
−−→
P
1
P
3
the three points lie on a straight line when
s
=
λ
r
where
λ
is a scalar.
If the points are
P
1
(0
,
−
2)
P
2
(1
,
−
1)
P
3
(4
,
2)
then
r
=
i
+
j
and
s
=4
i
+4
j
and
s
=4
r
therefore, the points lie on a straight line as confirmed by the diagram.
