Question 1: Express the translation of point A(3, 2) to point B(7, 5) as a column vector.

Answer: [4; 3]

Question 2: Calculate the column vector that translates point P(1, 4) to point Q(5, 7).

Answer: [4; 3]

Question 3: If a shape is translated by the vector [−2; 4], what is the new position of a point originally at (6, 3)?

Answer: [4; 7]

Question 4: Construct a translation that moves a point from (2, 3) to (8, 9). Write the column vector.

Answer: [6; 6]

Question 5: A triangle has vertices at (1,2), (4,2), and (1,5). If it is translated by the vector [3; −1], what are the new coordinates of the vertices?

Answer: Vertices after translation: (4,1), (7,1), (4,4)

Question 6: Plot the graph of y=2x and then translate the line by the vector [3; 4]. Describe the new position of the line.

Answer: The line y=2x shifts 3 units right and 4 units up, resulting in y=2x+8.

Question 7: A rectangle's bottom-left corner is at (2, 2). It is translated by the vector [5; -3]. What are the new coordinates of this corner?

Answer: [7; -1]

Question 8: Identify the mistake: A student claims that translating a point by [−3; 2] moves it from (5, 7) to (2, 9). Is this correct? If not, correct the translation.

Answer: Incorrect; translation should be from (5,7) to (2,9) with vector [−3; 2], which is correct. The mistake is the student might think the order matters. The translation vector [−3; 2] correctly moves (5,7) to (2,9).

Question 9: A parallelogram has vertices at (1,1), (4,1), (1,3), and (4,3). If it is translated by the vector [−2; 4], what are the new vertices?

Answer: Vertices after translation: (−1, 5), (2, 5), (−1, 7), (2, 7)

Question 10: Challenge: Construct a translation that moves the point (0, 0) to (7, −3). Write the column vector and describe the translation in words.

Answer: Vector: [7; −3]; the translation moves every point 7 units right and 3 units down.