5.3c Stating the Coordinates of the Image of a Point under a Combined Transformation

5.3c Stating the Coordinates of the Image of a Point under a Combined Transformation

1. The coordinates of the image of a point, K, under the combined transformation AB can be determined by the following steps.

Step 1:

Determine the coordinates of K’, the image of K, under the first transformation, B.

Step 2:

Determine the coordinates of K”, the image of K’, under the second transformation, A. K” is the image of K, under the combined transformation, AB.

Example:

T, P, R and E are four transformations that are defined as follows:

T = T r a n s l a t i o n (\begin{array}{l} - 4 \\ 3 \end{array})

P = Reflection in the y–axis.

R = Clockwise rotation 90^o about the origin

E = Enlargement with scale factor of 3 and the origin as centre.

Find the coordinates of the image of the point A (3, –2) under each of the following combined transformation.

(a) TT (b) PT (c) ET (d) ER (e) EP

Solution:

(a)

A(3, –2) → T → A’(–1, 1) → T → A”(–5, 4).

(b)

A(3, –2) → T → A’(–1, 1) → P → A”(1, 1).

(c)

A(3, –2) → T → A’(–1, 1) → E → A”( –3, 3).

(d)

A(3, –2) → R → A’(–2, 3) → E → A”( –6, –9).

(e)

A(3, –2) → P → A’(–3, –2) → E → A”( –9, –6).