J20

under the following combinations of transformations and state the
equivalent single transformation in each case:
(a) DE(OPQ) (b) FC(OPQ)
(c) DEC(OPQ) (d) DFE(OPQ)
5. Draw triangle XYZ at X(1, 2), Y(1, 6), Z(3, 6).
(a) Find the image of XYZ under each of the transformations BC and CB.
(b) Describe fully the single transformation equivalent to BC.
(c) Describe fully the transformation M such that MCB = BC.
Matrices of successive transformations
If each of the successive transformations has a transformation matrix, then a
single matrix that represents all the transformations can be obtained. Such a
matrix maps the original object onto the final image.
Example
M and N are transformations represented by matrices M =
1
1
2
and
3
1
0
N = . P is a point with coordinates (-1, 2).
2
1
(a) Find:
(i) M(P) (ii) N(P)
(iii) MN(P).
(b) If R is a transformation such that R = MN, find R(P). What can you deduce
from the results of (a) and (b)?
Solutions
1
2
1
3
(a) (i) M(P) is = .
1
3
2 5
P1(3, 5)
1
0
1
1
(ii) N(P) is =
2
1 2 0
P2(-1, 0)
1
1
2
1
(iii) MN(P) = M[N(P)] = M
=
0 1
3
0
1
=
1
1
2
1
0
5
2
(b) R = MN= =
1
3
2
1
7
3
5
2
1 1
R(P) = =
7
3
2 1