Question 1: Perform a translation of 3 units right and then a reflection across the x-axis on the point (2, 5). What are the coordinates of the final image?

Answer: (5, -5)

Question 2: Starting from the point (4, -3), first rotate 90° clockwise about the origin, then translate 2 units up. What are the new coordinates?

Answer: (3, 1)

Question 3: Construct a triangle with vertices at (1, 1), (4, 1), and (1, 4). Then, translate the triangle 2 units left and 3 units down. What are the new vertices?

Answer: (-1, -2), (2, -2), (-1, 1)

Question 4: A square with side length 5 units is reflected across the y-axis, then rotated 180° about the origin. What are the coordinates of its vertices if one vertex was initially at (3, 4)?

Answer: (-3, -4)

Question 5: In a real-world scenario, a sculpture is moved by first translating 4 meters east and then rotating 45° clockwise around a base point. Describe the two-step transformation applied to the sculpture's position.

Answer: The sculpture is shifted 4 meters east, then rotated 45° clockwise around the base point to reach its new position.

Question 6: A triangle has vertices at (0, 0), (6, 0), and (0, 8). It is translated 3 units right and then reflected across the x-axis. What are the new vertices?

Answer: (3, 0), (9, 0), (3, -8)

Question 7: A rectangle is rotated 90° clockwise about its bottom-left corner, then translated 2 units up. Describe the overall transformation applied.

Answer: The rectangle is first rotated 90° clockwise about its bottom-left corner, then moved 2 units upward.

Question 8: A point at (−2, 3) undergoes a 180° rotation about the origin, then a translation 5 units left. What are its final coordinates?

Answer: (3, -3)

Question 9: Identify and correct the mistake in this transformation sequence: translating a point (1,2) 4 units right, then rotating 90°, but the final coordinates are incorrectly given as (−2, 5).

Answer: Correct sequence: (1, 2) → (5, 2) after translation, then rotate 90° clockwise to (2, -5). The correct final coordinate should be (2, -5), not (−2, 5).

Question 10: Challenge: A hexagon is first reflected across the y-axis, then rotated 60° counter-clockwise about its center. Describe the combined effect of these two transformations.

Answer: The hexagon is reflected across the y-axis, flipping it horizontally, then rotated 60° counter-clockwise around its center, changing its orientation and position.