Combinations of Transformations (HSC SSCE Mathematics Advanced): Flashcards
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Definition of commuting transformations
Definition of commuting transformations
Transformations producing same result regardless of order applied
Two translations commute?
Two translations commute?
Yes, order doesn't matter
Two dilations commute?
Two dilations commute?
Yes, order doesn't matter
Cross-direction transformations commute?
Cross-direction transformations commute?
Yes (e.g., horizontal dilation + vertical translation)
Same-direction translation & dilation commute?
Same-direction translation & dilation commute?
No, order matters and produces different results
Universal formula for transformations
Universal formula for transformations
Reflection in axes as dilation factor
Reflection in axes as dilation factor
When does order of transformations matter?
When does order of transformations matter?
When both act in same direction (both horizontal or vertical)
Horizontal translation + horizontal dilation commute?
Horizontal translation + horizontal dilation commute?
No, order matters
Vertical translation + vertical dilation commute?
Vertical translation + vertical dilation commute?
No, order matters
