J20

From the results of (a) and (b), MN(P) = R(P).
Example
Draw ∆PQR with vertices P(3, 1), Q(6, 1) and R(6, 5).
(a) Draw the image of ∆PQR under the transformation represented by the
0
1
matrix , label it P 1Q 1R 1 and describe this transformation fully.
1
0
(b) Draw the image of ∆ P 1Q 1R 1 under a rotation of 180 0 about the origin and
label it P 2Q 2R 2. Find the matrix that represents this transformation.
(c) Describe fully the single transformation that maps ∆PQR onto ∆ P 2Q 2R 2.
Find the matrix that represents this transformation.
Solutions
(a)
P Q R P 1 Q 1 R 1
0
1 3
6 6
1
1 5
=
1
0
1
1 5 3
6 6
The transformation is a reflection in the line y = x.
(b) The image of ∆ P 1Q 1R 1 is ∆ P 2Q 2R 2 as shown in the figure below.
1
0
is the matrix representing this transformation. This is a half-turn
0 1
about (0, 0).
(c) From the diagram, the single transformation that maps ∆PQR onto
∆ P 2Q 2R 2 is a reflection in y = -x.
Under a reflection in y = -x, the identity matrix
I J I 1 J 1
0
1
1
0
1
0
maps onto . Therefore, is the matrix that maps
1
0
0 1
0 1
∆PQR onto ∆ P 2Q 2R 2