**3.1d Describing the Combination of Two Transformations Given the Object and the Image**

In the diagram above, triangle

*KLM*is the image of triangle*ABC*under the combined transformations*VW*. Describe in full, the transformation*W*and the transformation*V.*
Figure

*ABC*→**→ Figure***W**KB’C’*→**V**→ Figure*KLM*

$W=\text{Translation}\left(\begin{array}{l}0\\ 4\end{array}\right)$

**= Enlargement with centre**

*V**K*(1, 1) and a scale factor of 3.

**Example 2:**

In the diagram above, triangle

*CKL*is the image of triangle*ABC*under the combined transformations*UY*. Describe in full, the transformation*Y*and the transformation*U.*

*Solution:*Figure

*ABC*→**→ Figure***Y**AB’C*→**→ Figure***U**CKL*

*Y**= Reflection in the straight line*

*y*= 6

**= Enlargement with centre**

*U**C*(12, 6) and a scale factor of 2.

**Example 3:**

In the diagram above, triangle

*PQR*is the image of triangle*ABC*under the combined transformations*TW*. Describe in full, the transformation*W*and the transformation*T.*

*Solution:*Figure

*ABC*→**→ Figure***W**PBC’*→**→ Figure***T**PQR*

*W**= Clockwise rotation of 90*

^{o}about the point

*B*(5, 5)

**= Enlargement with centre**

*T**P*(1, 5) and a scale factor of 2.