**3.2 Solving Problems involving Transformations**

**Example:**

**(a)**Transformation

**is a translation $\left(\begin{array}{l}\text{}5\\ -2\end{array}\right)$**

*T*
Transformation

**is a reflection in the straight line***P**y*= 7.
State the coordinates of the image of point

*A*under each of the following transformations:**(i)**Transformation

**,**

*T***(ii)**Combined transformation

**.**

*PT*

**(b)**

**(i)**

*PQR*is the image of triangle

*ABC*under the combined transformations

*MN*. Describe in full, the transformation

*N*and the transformation

*M.*

**(ii)**Given that the area of the shaded region

*PSTR*is 200 m

^{2}, calculate the area of the triangle

*SQT*.

*Solution:***(a)**

**(ii)**

*A*(3, 11) →

**→**

*T**A’*(8, 9) →

**→**

*P**A”*(8, 5).

**(b)(i)**

**= Enlargement with centre (5, 12) and a scale factor of 3.**

*M*

**(c)**

Area of image = (Scale factor)

^{2}x Area of object
Area of

*PQR*= 3^{2}x Area of*SQT*
Area of

*SQT*+ Area of*PSTR*= 9 x Area of*SQT*
Area of

*SQT*+ 200 = 9 x Area of*SQT*
200 = 9 x Area of

*SQT*– Area of*SQT*
200 = 8 x Area of

$\text{Areaof}SQT=\frac{200}{8}$
*SQT***Area of**

*SQT*= 25 m^{2}