5
QuizMultiple Select

Congruence and Transformations — Unit test

Question 5 • SRC 2022 M/J Grade 8 Pre-Algebra Q1

Which sequence of transformations would result in an image that is similar and non-congruent to the pre-image? Assume that any scale factor for the dilations is not equal to 1. Check all that apply.

Answer
A
a dilation followed by a translation
B
a dilation followed by a reflection
C
a reflection followed by a dilation
D
a rotation followed by a reflection
E
a rotation followed by a dilation
F
a translation followed by a reflection

Explanation

A dilation with a scale factor other than 1 changes the figure’s size while preserving its shape, so the result is similar but not congruent. Translations, reflections, and rotations preserve size, so combining any of them with a dilation still gives a similar, non-congruent image. Thus the sequences in choices A, B, C, and E work; choices D and F use only size-preserving transformations.

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