Question 1: Write the column vector that represents a translation 3 units to the right and 2 units up.

Answer: [3; 2]

Question 2: Construct a translation of point A (2, 5) by the vector (−4; 3). What are the coordinates of the new point?

Answer: (-2, 8)

Question 3: Plot the graph of y=2x and illustrate the translation by the vector (4; -2).

Answer: Students plot the line and shift it accordingly.

Question 4: A triangle has vertices at (1, 2), (4, 3), and (2, 5). Translate the triangle using the vector (3; -1). What are the new coordinates?

Answer: Vertices at (4, 1), (7, 2), (5, 4)

Question 5: If a shape is translated 5 units left and 4 units down, what is the translation vector?

Answer: (-5, -4)

Question 6: Explain why the translation vector (0; 0) leaves the object unchanged.

Answer: Because it shifts the object by zero units in both directions, so it remains in the same position.

Question 7: A shape is translated by the vector (−2; 5). If the original shape's coordinates are (3, 4), what are the new coordinates?

Answer: (1, 9)

Question 8: Identify the mistake in the following translation: A point (2, 3) was translated by the vector (4; -2), but the resulting point was given as (6, 1).

Answer: The correct translation is (6, 1), so the student made no mistake; the answer is correct.

Question 9: A square with vertices at (1, 1), (3, 1), (3, 3), and (1, 3) is translated by the vector (2; 4). Write the new coordinates of all vertices.

Answer: Vertices at (3, 5), (5, 5), (5, 7), (3, 7)

Question 10: A design pattern is translated 6 units right and 3 units down. If the original position of a point is at (−1, 2), what is its new position?

Answer: (5, -1)

Question 11: Challenge: Given a shape translated by the vector (−3; 5), find the original coordinates if the translated shape has a point at (4, 10).

Answer: (7, 5)