**3.1c 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**can be determined by the following steps.

*AB*

*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:

$T=Translation\text{}\left(\begin{array}{l}-4\\ \text{}3\end{array}\right)$

*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)**

**(b)**

**(c)**

*A*(3, –2) →

**R**→

*A’*(–2, 3) →

**E**→

*A”*( –6, –9).

*A*(3, –2) →

**P**→

*A’*(–3, –2) →

**E**→

*A”*( –9, –6).