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
 
Example 1:

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.

Solution:


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

W = Translation ( 0 4 )   
= Enlargement with centre (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
= Enlargement with centre (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 (5, 5)
= Enlargement with centre (1, 5) and a scale factor of 2.

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