Question 1: A figure is translated 4 units right and then reflected across the y-axis. Describe the single transformation equivalent to these two steps.

Answer: Reflection across y-axis with translation of 4 units right

Question 2: Calculate the combined transformation of rotating 90° clockwise followed by translating 3 units down.

Answer: Rotation + translation (see explanation)

Question 3: A figure is reflected across the x-axis and then rotated 180°. What single transformation results in this sequence?

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

Question 4: Construct a transformation sequence where a figure is translated 2 units left and then rotated 90° counterclockwise. Describe the single transformation.

Answer: A rotation combined with translation, equivalent to a single transformation depending on context

Question 1: A triangle undergoes a reflection across the y-axis, then a translation 5 units up, and finally a 180° rotation around the origin. Describe the single transformation equivalent and justify your answer.

Answer: A composition of reflection, translation, and rotation; combined into a single transformation depends on properties.

Question 2: Determine the single transformation that combines a 270° clockwise rotation and a horizontal translation of 6 units to the right. Show your working.

Answer: A 90° rotation combined with translation; specific details depend on transformation rules

Question 3: Explain why combining two reflections across intersecting lines results in a rotation, and specify the angle of rotation.

Answer: The angle is twice the angle between the lines; reasoning based on geometric properties.

Question 4: A translation 3 units left is followed by a reflection across the y-axis. Find the single transformation that achieves this.

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

Question 1: A robot moves 5 units forward, then turns 90° clockwise and moves 3 units. Describe the single transformation needed for the robot to return to its original position from its last point.

Answer: A rotation + translation; specific details depend on movement

Question 2: A drone shifts 10 meters east, then flips vertically over a horizontal axis. What is the equivalent single transformation?

Answer: Vertical reflection combined with translation eastward

Question 1: A shape undergoes a translation 2 units right, a reflection across the x-axis, then a rotation 270° clockwise about the origin. Find the single transformation that combines all these steps.

Answer: A composition of translation, reflection, and rotation; reducible to a specific rotation or reflection depending on sequence

Question 2: Prove that a reflection across a line followed by a rotation about the same point results in a different transformation. Use an example with specific angles.

Answer: Depends on angles; generally, reflection + rotation ≠ single reflection unless lines are specific

Question 1: A figure is rotated 180°, then translated 4 units down. Describe the single transformation equivalent.

Answer: Rotation 180° with translation downward

Question 2: A reflection across the y-axis is followed by a translation 2 units right. What is the combined transformation?

Answer: Reflection across y-axis with translation right

Question 1: A student combines a reflection across the x-axis and then a translation 3 units left, but claims the result is just a reflection across the x-axis. Explain the mistake and correct it.

Answer: The student overlooked the translation; the correct combined transformation includes both reflection and translation.

Question 2: A student rotates a shape 90° counterclockwise and then reflects it across the y-axis, believing this is a single transformation. Is this correct? Explain.

Answer: Incorrect; this sequence results in a different transformation, not a single equivalent transformation.