J20

Alternatively, this transformation is a successive transformation of a reflection in
y = x followed by a rotation of 180 0 about the origin. Thus, a single matrix is
obtained from the product of the two matrices as:
1
0
0
1 0 1
=
0 1
1
0
1
0
When multiplying, the matrix of the first transformation (in this case reflection in
y = x) is to the right of the matrix of the second transformation (in this case
rotation of 180 0 about the origin)
Exercise
1. Find a single matrix that represents the following successive transformations.
(a) A reflection in the x-axis followed by a reflection in the y-axis.
(b) A reflection in the line y = x followed by a reflection in the line
y = -x.
(c) A clockwise rotation of 90 0 about the origin followed by an enlargement of
scale factor 3 with the centre of enlargement as the origin.
(d) An enlargement of factor 2 with centre O followed by an anticlockwise
rotation of 90 0 about O.
2. Draw the parallelogram formed by the points P(1, -3), Q(4, -3), R(6, 1) and
S(3, -1).
(a) Draw the image P1Q1R1S1 of the parallelogram after a reflection in the line y
= 0.
(b) Reflect the image in the line y = x to obtain parallelogram P2Q2R2S2.