Graphics Reference
In-Depth Information
Y
P
1
n
Q
O
1
X
Fig. 12.9.
Q
is the nearest point on the line to
P
.
12.10 Position of a Point Reflected in a Line
Suppose that instead of finding the nearest point on the line we require the
reflection
Q
of
P
in the line. Once more, we set out to discover the position
vector for
Q
.
Figure 12.10 shows the vectors used in the analysis. We start with the line
equation
ax
+
by
+
c
=0
and declare
T
(
x, y
) as the nearest point on the line to
O
with
t
=
x
i
+
y
j
as
its position vector.
From the line equation
n
=
a
i
+
b
j
therefore
.
n
t
=
−
c
(12.8)
Y
n
P
r
T
r
+
r
′
r
′
t
p
Q
q
O
X
Fig. 12.10.
The vectors required to find the reflection of
P
in the line.
