Question 1: Calculate the coordinates of a point that is first translated 3 units right and then reflected across the x-axis from the point (2, 5).

Answer: 2, -5

Question 2: A shape is rotated 90° clockwise around the origin and then translated 4 units up. If a point on the shape originally is at (1, 2), where is it after these transformations?

Answer: 4, -1

Question 3: Perform a reflection of the point (-3, 4) across the y-axis and then translate it 5 units left. What are the new coordinates?

Answer: -1, 4

Question 4: Plot the point (3, -2) and perform a translation 2 units down and then a horizontal reflection across the y-axis. Write the final coordinates.

Answer: -3, -2

Question 1: A triangle with vertices at (2, 3), (4, 5), and (6, 3) undergoes a translation 3 units left and then a reflection across the x-axis. What are the new coordinates of the vertices?

Answer: (-1, -3), (1, -5), (3, -3)

Question 2: A rectangle is rotated 180° about the origin and then translated 5 units right. If one vertex is at (1, -2), where is it after the transformations?

Answer: 6, 2

Question 3: A point is reflected across the y-axis and then rotated 90° counter-clockwise about the origin. Starting at (5, -3), find its final position.

Answer: -3, -5

Question 4: A shape is translated 4 units up and then reflected across the x-axis. If a point on the shape is at (-2, 1), where does it end up?

Answer: -2, -1

Question 5: Explain the steps needed to transform a point from (0, 0) to (-4, 3) using only two transformations. Justify your answer.

Answer: One possible way: translate (-4, 3), then reflect across the y-axis.

Question 1: A map shows a city block with a corner at (x, y). The map is moved 100 meters east and then flipped across a central street running north-south. If the original corner is at (200, 300), where is it after these transformations?

Answer: 300, -200

Question 2: A drone is programmed to fly 150 meters forward and then turn 90° right, moving another 50 meters. Show the final position starting from (0, 0).

Answer: 150, 50

Question 1: A square is translated 5 units right, rotated 90° clockwise about its center, and then reflected across the x-axis. If a vertex starts at (2, 3), where is it after all transformations?

Answer: 8, -3

Question 2: Construct a polygon that, after two transformations—first a reflection across the y-axis and then a translation 4 units down—ends with a vertex at (2, -1). What are the original coordinates?

Answer: (-2, 3)

Question 1: A point is translated 7 units left and then reflected across the y-axis. Starting from (3, 4), where is it now?

Answer: -10, 4

Question 2: A shape is rotated 180° about the origin and then translated 2 units down. If a point on it is at (-4, 5), where does it land?

Answer: 4, -3

Question 1: A student performs a translation 3 units right and then a reflection across the x-axis on point (1, 2), but gets (-1, -2). Identify the mistake and correct the process.

Answer: Mistake: The student reflected across the y-axis instead of the x-axis. Correct: Reflection across the x-axis changes (x, y) to (x, -y).