The order in which the two transformations in a composite transformation affect the final answer
To determine if order matters or not, I will use the following example and illustration.
Let the coordinate of point A be:
A = (2, 5)
Perform the following transformations:
First order: Translation before dilation
The translation by (x, y + 1) would give:
A' = (2, 5 + 1)
A' = (2,6)
The dilation by a scale factor of 2 would give
A" = 2 * (2,6)
A" = (4,12)
Second order: Dilation before translation
The dilation by a scale factor of 2 would give
A' = 2 * (2,5)
A' = (4,10)
The translation by (x, y + 1) would give:
A'' = (4, 10 + 1)
A'' = (4,11)
See that the final coordinates in both orders are not the same.
Hence, the order in which the two transformations in a composite transformation affect the final answer
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