Question 1: A shape is rotated 90° clockwise around the origin, then translated 4 units to the right and 2 units up. What single transformation maps the original shape directly to its final position?

Answer: Rotation 90° clockwise combined with translation (4 right, 2 up)

Question 2: Construct a triangle on the grid, then perform a reflection across the y-axis and a translation 3 units left. Describe the single transformation equivalent to these two transformations.

Answer: Reflection across y-axis combined with translation 3 units left

Question 3: A shape undergoes a translation 5 units down followed by a 180° rotation around the origin. What is the single transformation that produces the same result?

Answer: Rotation 180° followed by translation 5 units down

Question 4: Fluency & Practice: If a figure is translated 3 units right and 4 units up, then reflected across the x-axis, what single transformation is equivalent to these combined steps?

Answer: Translation (3 right, 4 up) then reflection across x-axis

Question 5: A shape is rotated 270° clockwise and then translated 2 units left. Find the single transformation that maps the original shape to its final position.

Answer: Rotation 270° clockwise (or 90° counterclockwise) combined with translation 2 units left

Question 6: A rectangle is reflected across the y-axis and then rotated 180° around the origin. Describe the single transformation equivalent to these two steps.

Answer: Reflection across y-axis followed by rotation 180°

Question 7: Problem Solving & Reasoning: A figure is translated 4 units right and 3 units down, then reflected across the y-axis. What is the combined single transformation? Explain your reasoning.

Answer: Reflection across y-axis combined with translation 4 units right and 3 units down; in total, equivalent to reflection across y-axis and translation 4 units right, 3 units down.

Question 8: A shape undergoes a rotation of 180° and then a translation 3 units up. What single transformation achieves the same effect?

Answer: Rotation 180° followed by translation 3 units up

Question 9: Construct a shape and perform the following: reflect across the x-axis, then rotate 90° clockwise. Describe the single transformation equivalent to these two steps.

Answer: Rotation 90° clockwise followed by reflection across x-axis

Question 10: Error Analysis: A student claims that performing a reflection across the y-axis followed by a translation 2 units left is the same as a reflection across the x-axis followed by translation 2 units left. Is this correct? Explain your reasoning and correct if necessary.

Answer: Incorrect. Reflection across y-axis and reflection across x-axis are different; the order matters. The correct combined transformation is reflection across y-axis plus translation 2 units left.