A sequence of transformations is applied to a polygon. Which of the following statements represent a sequence of transformations where the resulting polygon is similar to the original polygon but has a smaller area than the original polygon? Select all that apply.

A. a reflection over the y-axis followed by a translation of 10 units down and a dilation about the origin by a scale factor of 2 B. a rotation of 180° counterclockwise about the origin followed by a dilation about the origin by a scale factor of 5 2 C. a dilation about the origin by a scale factor of 2 3 followed by a rotation of 90° counterclockwise about the origin and a translation 5 units left D. a dilation about the origin by a scale factor of 5 7 followed by a reflection over the y-axis and a dilation about the origin by a scale factor of 3 4

Question

Mathematics

Adelyn Waller

1 January, 12:42

A sequence of transformations is applied to a polygon. Which of the following statements represent a sequence of transformations where the resulting polygon is similar to the original polygon but has a smaller area than the original polygon? Select all that apply.

A. a reflection over the y-axis followed by a translation of 10 units down and a dilation about the origin by a scale factor of 2 B. a rotation of 180° counterclockwise about the origin followed by a dilation about the origin by a scale factor of 5 2 C. a dilation about the origin by a scale factor of 2 3 followed by a rotation of 90° counterclockwise about the origin and a translation 5 units left D. a dilation about the origin by a scale factor of 5 7 followed by a reflection over the y-axis and a dilation about the origin by a scale factor of 3 4

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Answers (1)

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Gustavo Blanchard · Answer 1

C, D

Step-by-step explanation:

Any rigid transformation (rotation, translation, reflection) will result in a congruent polygon. To make a similar (smaller) polygon, a dilation by a factor less than 1 must be used.

C. a dilation about the origin by a scale factor of 2/3 followed by a rotation of 90° counterclockwise about the origin and a translation 5 units left

D. a dilation about the origin by a scale factor of 5/7 followed by a reflection over the y-axis and a dilation about the origin by a scale factor of 3/4