Translations, Rotations, and Reflections Review

Question 1.

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.

Figure Q was the result of a sequence of transformations on figure P, both shown.

Which sequence of transformations could take figure P to figure Q?

• reflection over the x-axis and translation 7 units right

• reflection over the y-axis and translation 3 units down

• translation 1 unit right and 180⁰ rotation about the origin

• translation 4 units right and 180⁰ rotation about the origin

Square PQRS and TUVW are show below.

Which sequence of transformations of square PQRS shows that square PQRS is congruent to square TUVW?

• a translation 2 units up and 2 units to the right, then a reflection over the x-axis

• a translation 2 units up and 2 units to the right, then a reflection over the y-axis

• a translation 2 units down and 2 units to the left, then a reflection over the x-axis

• a translation 2 units down and 2 units to the left, then a reflection over the y-axis

Triangle F and triangle G are shown below.

Which sequence does NOT transform triangle F to triangle G?

• a 180⁰ clockwise rotation about the origin

• a 180⁰ 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 90⁰ clockwise rotation about the origin.

On the coordinate plane below, rectangle ABCD is rotated 90^o clockwise about the origin to form rectangle WXYZ.

Which statement about the relationship between rectangle ABCD and rectangle WXYZ is true?

• 
• 
• 
• 

Figure L and figure M are shown on the grid below.

Maria wants to transform figure L to figure M using only rotations, reflections, and translations. Which statement is true?

• The transformation can be done with a reflection followed by a rotation.

• The transformation can be done with a reflection followed by a translation.

• The transformation cannot be done because figure L is not congruent to figure M.

• The transformations cannot be done because figures L and M are in different quadrants

In which pair of figures can figure A be taken to figure B by a rotation?

• Pair 1

• Pair 2

• Pair 3

• Pair 4

Lily wants to define a transformation (or series of transformation) 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 by two reflections.

• It can be defined with one rotation 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.

A parallelogram with vertices at (0, 3), (2, 0), (4, 2), and (2, 5) is reflected over the y-axis. Which vertex of the parallelogram will have the same x-coordinate before and after the reflection?

• (0,3)

• (2,0)

• (4,2)

• (2,5)

In the diagram below, lines MN and JK are parallel and are intersected by line QT.

Which transformation could be used to show that angle MRS is congruent to angle JST?

• reflect angle MRS over the x-axis

• rotate angle MRS about the origin

• translate angle MRS down and to the right

• dilate angle MRS by a scale factor of two with the center at point R