J20

An object can undergo several transformations, one after the other. This is
done such that the image of the preceding transformation becomes the object
of the next transformation.
When a object, A, undergoes a transformation R followed by another
transformation N, this is shown as N[R(A)] or NR(A).
The first transformation is always indicated to the right of the second
transformation.
RR(A) means ‘perform transformation R on A and then perform R on the
image’. It may be written R 2 (A).
Example
A is a triangle with vertices (2, 1), (2, 4) and (4, 1). R is a rotation of 90 0
clockwise about the origin and N is a reflection in the y-axis. Find the vertices of
the image of A if it undergoes the following transformations:
(a) NR(A) (b) RN(A)
Solution
(a) The figure below shows triangle A under these transformations and its
image R(A) and NR(A).
The final image of A has vertices (-1, -2), (-1, -4) and (-4, -2).
(b) The figure below shows triangle A and its images N(A) and RN(A).
The final image of triangle A under these transformations has vertices
(1, 2), (1, 4) and (4, 2).
The order of transformation is very important.
NR(A) ≠ RN(A).