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

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 and the transformation V.
Figure ABC W→ Figure KB’C’ V → Figure KLM

$W=\text{Translation}\left(\begin{array}{l}0\\ 4\end{array}\right)$
V= Enlargement with centre 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 and the transformation U.

Solution:
Figure ABC Y→ Figure AB’C U → Figure CKL
Y = Reflection in the straight line y = 6
U= Enlargement with centre 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 and the transformation T.

Solution:
Figure ABC W→ Figure PBC’ T → Figure PQR
W = Clockwise rotation of 90o about the point B(5, 5)
T= Enlargement with centre P(1, 5) and a scale factor of 2.