Congruence and Transformations

Question 1

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

Revolt · Accepted Answer

a reflection across the x-axis followed by another reflection across the x-axis; a rotation of 180 degrees followed by another rotation of 180 degrees; a translation to the right followed by an equal translation to the left; a rotation 90° about the origin followed by a counter-clockwise rotation 90° about the origin

Question 2

Do you think a sequence of translations across the x- or y-axis and/or reflections on a figure could result in the same image as a 90-degree clockwise rotation? Explain why or why not.

Revolt · Accepted Answer

No, it is not possible. A 90-degree clockwise rotation changes the position of the x- and y-coordinates (transforming (x, y) into (y, -x)). Translations and reflections across the x- or y-axis only change the signs or values of the coordinates, but they cannot swap the order of the x and y values itself. Therefore, you cannot achieve the same result as a rotation using only these transformations.

Question 3

Check all that you included in your response.

Revolt · Accepted Answer

It is not possible.; The coordinates need to be reversed.; You cannot reverse coordinates using only reflections and translations.

Congruence and Transformations Answers

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