Rigid Transformations and Congruence Review

Figure X and figure Y are shown on the coordinate grid below. Which statement about figures X and Y must be true?

• A series of translations will transform figure X to figure Y, and the figures will be congruent.

• A 180 degree clockwise rotation will transform figure X to figure Y, and the figures will be congruent.

• A series of translations will transform figure X to figure Y, but the figures will not be congruent.

• A 180 degree clockwise rotation will transform figure X to figure Y, but the figures will not be congruent.

Pentagon P and pentagon Q, shown in the picture, are congruent. Which sequence could be used to transform pentagon P to pentagon Q?

• A 180 degree clockwise rotation about the origin

• A translation four units left and then a reflection over the x-axis.

• A reflection over the y-axis and then a translation seven units down.

• A translation seven units down and then a 90 degree clockwise rotation about the origin.

Triangle F and triangle G are shown in the picture. Which sequence does not transform triangle F to triangle G?

• A 180 degree clockwise rotation about the origin.

• A 180 degree counterclockwise rotation about the origin.

• A reflection over the x-axis and then a reflection over the y-axis.

• A reflection over the y-axis and then a 90 degree clockwise rotation about the origin.

Triangle A and triangle B are graphed on the coordinate plane shown. Which sequence of transformations will map triangle A onto its congruent image, triangle B?

• A reflection over the x-axis, then a reflection over the y-axis.

• A translation 8 units down, then a reflection over the y-axis.

• A reflection over the x-axis, then a translation 6 units to the left.

• A rotation 90 degrees about the origin, then a translation 6 units to the left.

Congruent rectangles HJKL and H'J'K'L' are shown on the coordinate grid in the picture. Describe a sequence of transformations on rectangle HJKL that would result in rectangle H'J'K'L'.

Evaluate responses using AI:

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Lily wants to define a transformation (or series of transformations) using only rotations, reflections, or translations that takes Figure A to Figure B. Which statement about the transformation that Lily wants to define is true?

• It can be defined with two reflections.

• It can be defined with one rotations and one translation.

• It cannot be defined because Figure A and Figure B are not congruent.

• It cannot be defined because the longest side of figure B is on the bottom.

• Translation

• Reflection

• Rotation

• Dilation

• a single reflection

• a single rotation

• a single translation

• a translation, then a reflection

• a reflection, then a different reflection

• Pair 1

• Pair 2

• Pair 3

• Pair 4

Which of these sequences of transformations would not return a shape to its original position?

• Translate 3 units up, then 3 units down

• Reflect over line p, then reflect over line p again

• Translate 1 unit to the right, then 4 units to the left, then 3 units to the right

• Rotate 120 degrees counterclockwise around Center C, then rotate 220 degrees counterclockwise around C again.