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

*KLM*is the image of triangle

*ABC*under the combined transformations

*VW*. Describe in full, the transformation

*W*and the transformation

*V.*

*ABC*→

**→ Figure**

*W**KB’C’*→

**V**→ Figure

*KLM*

**= 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.