Unit 3 Test Review: Transformations

If △ABC is rotated 90° clockwise about the origin, what will be the new coordinates of vertex B?

• (-1, -4)

• (1, 4)

• (4, 1)

• (4, -1)

A figure is located entirely in the third quadrant. If it is reflected over the y-axis, in which quadrant will its image lie?

• Quadrant I

• Quadrant II

• Quadrant III

• Quadrant IV

Which of the following transformations may not map the pre-image to a congruent image?

• dilation

• rotation

• translation

• reflection

Quadrilateral ABCD is graphed on a coordinate plane, with point C plotted at (-4,3). Quadrilateral ABCD is then reflected over the y-axis to create its image A'B'C'D'. After the reflection, what are the coordinates of point C'?

• (4,3)

• (4,-3)

• (-4,3)

• (-4,-3)

Write a description of the rule (x, y) → (x - 3, y + 4)

• translation 3 units down and 4 units right

• translation 3 units to the left and 4 units up

• translation 3 units to the left and 4 units down

• translation 3 units to the right and 4 units up

Figure Q was the result of a sequence of transformations on figure P, both shown below. 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 180° rotation about the origin

• translation 4 units right and 180° rotation about the origin

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

Rectangle R undergoes a dilation with scale factor 2 and then a reflection over the y-axis. The resulting image is Rectangle S. Which statement about Rectangles R and S is true?

• They are congruent and similar.

• They are similar but not congruent.

• They are congruent but not similar.

• They are neither congruent nor similar.

The area of triangle KLM is 32 square units. After a 270° counterclockwise rotation about the origin, the area of image KLM is

• 8 square units

• 16 square units

• 24 square units

• 32 square units

Answer explanation

Remember that a rotation creates congruent figures (same size and shape) so the area will remain the same.

A sequence of transformations was applied to an equilateral triangle in a coordinate plane. The transformations used were rotations, reflections, and translations. Which statement about the resulting figure is true?

• It must be an equilateral triangle with the same side lengths as the original triangle.

• It must be an equilateral triangle, but the side lengths may differ from the original triangle.

• It may be a scalene triangle, and all the side lengths may differ from the original triangle.

• It may be an obtuse triangle with at least one side the same length as the original triangle.