13
AssignmentMultiple Select

Congruence and Transformations

Question 13 • HCISD-Mathematical Models with Applications B-CR SUMMER

Choose all sequences of transformations that produce the same image of a given figure.

Answer
A
a reflection across the x-axis followed by another reflection across the x-axis
B
a reflection across the y-axis followed by a counter-clockwise rotation 90° about the origin
C
a rotation of 180 degrees followed by another rotation of 180 degrees
D
a translation to the right followed by an equal translation to the left
E
a clockwise rotation 90° about the origin followed by a counter-clockwise rotation 90° about the origin

Explanation

A transformation followed by its inverse returns a figure to its original position. Reflecting twice across the x-axis, rotating 180° twice, and translating right then an equal distance left each undo the first move. A clockwise 90° rotation followed by a counter-clockwise 90° rotation also returns the figure to its starting position. Choice B does not undo its reflection, so it generally produces a different image.

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