Congruence and Transformations

Question 1

The final image is the same as which of the following transformations?

Revolt · Accepted Answer

Translate 5 units down, and then reflect over the y-axis.

Question 2

The final image is the same as what single transformation?

Revolt · Accepted Answer

a 180° rotation about the origin

Question 3

Which sequence of transformations produces [image 1] L'M'N' from [image 2] LMN?

Revolt · Accepted Answer

a translation 5 units down and 2 units to the right followed by a reflection across the y-axis

Question 4

45✔ 90180270

Revolt · Accepted Answer

✔ 90; A clockwise rotation ° about the origin followed by a translation units to the right and 6 units down produces ΔX'Y'Z' from ΔXYZ.: 90; A clockwise rotation ° about the origin followed by a translation units to the right and 6 units down produces ΔX'Y'Z' from ΔXYZ.: 2

Question 5

1✔ 246

Revolt · Accepted Answer

✔ 2

Question 6

a reflection across the y-axis followed by a clockwise rotation 90° about the origina reflection across the x-axis, followed by a counter-clockwise rotation 90° about the origin, followed by a translation 4 units down and 4 units to the lefta counter-clockwise rotation of 90° about the origin followed by a translation 4 units to the rightno sequence of translations, rotations, and reflections because the images are not congruent

Revolt · Accepted Answer

no sequence of translations, rotations, and reflections because the images are not congruent

Question 7

Santana says the image is formed from the pre-image by a reflection across the y-axis followed by a translation 2 units to the right, in that order. Is Santana’s thinking correct?

Revolt · Accepted Answer

Santana’s reasoning is not correct. The translation should be 2 units to the left, not to the right.

Question 8

Check all that you included in your response.

Revolt · Accepted Answer

Santana’s reasoning is not correct.; The translation should be 2 units to the left.

Question 9

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 clockwise rotation 90° about the origin followed by a counter-clockwise rotation 90° about the origin

Question 10

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.

Congruence and Transformations Answers

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