3.1d Describing the Combination of Two Transformations Given the Object and the Image
Example 1:
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.
Solution:
Figure ABC → W→ Figure KB’C’ → V → Figure KLM
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 Y 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 W 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.