Transformations and Congruence Review

The trapezoid in figure A is transformed to trapezoid A' as shown below. What sequence of transformations will prove them congruent?

• Reflection about the y-axis and rotation of 90° counterclockwise about the origin.

• Reflection about the x-axis and rotation of 90° counterclockwise about the origin.

• Reflection about the y-axis and rotation of 180° counterclockwise about the origin.

• Reflection about the x-axis and rotation of 180° counterclockwise about the origin.

Two figures are shown in the graph. Figure 1 is transformed into figure 2. What transformations have occurred?

• rotation of 180° clockwise

• rotation of 180° counterclockwise

• reflection over the x-axis, reflection over the y-axis

• reflection over the x-axis, rotation 90° clockwise about the origin

Which series of transformations does NOT prove that triangle in figure A is congruent to the triangle in figure A'?

• a reflection across the x-axis followed by a 90° clockwise rotation about the origin

• a reflection across the y-axis followed by a 180° clockwise rotation about the origin

• a reflection across the y-axis followed by a 90° counterclockwise rotation about the origin

• a reflection across the x-axis followed by a 270° counterclockwise rotation about the origin

The graph below shows parallelogram R'S'T'U' after a 90° counterclockwise rotation about the origin. What were the coordinates of parallelogram RSTU?

• R(-6, 3), S(-2, 3), T(-4, 5), and U(-8, 5)

• R(3, -6), S(3, -2), T(5, -4), and U(5, -8)

• R(-3, 6), S(-3, 2), T(-5, 4), and U(-5, 8)

• R(6, -3), S(2, -3), T(4, -5), and U(8, -5)

Which set of transformations could be applied to figure A to prove that it is congruent to figure A'?

• reflection across the y-axis and translation down 2 units

• reflection across the y-axis and translation down 6 units

• rotation of 180° about the origin, followed by a reflection across the x-axis

• rotation of 90° clockwise about the origin, followed by a reflection across the x-axis

Parallelogram ABCD was translated to parallelogram A'B'C'D'. How many units and in which direction were the x-coordinates of parallelogram ABCD moved?

• 3 units to the right

• 3 units to the left

• 7 units to the right

• 7 units to the left

A shape is shown below. Which shows this shape transformed by a flip?

• Option A

• Option B

• Option C

• Option D

Which of the following is a single reflection of figure N over the y-axis to form N'?

• A

• B

• C

• D

Which figure shows the triangle below reflected over the x-axis, then reflected over the y-axis?

• A

• B

• C

• D

Figure EFGH in the coordinate plane has vertices at (-5, 2), (-5, -2), (-1, -2), and (-1, 2). If the figure is translated 5 units to the right and 2 units up, what are the coordinates of the E'F'G'H'?

• (0, 4), (0, 0), (4, 0), (4, 4)

• (-3, 7), (-3, 3), (1, 3), (1, 7)

• (-10, 0), (-10, 4), (-6, -4), (-6, 0)

• (-7, -3), (-7, -7), (-3, -7), (-3, -3)