Question 1: If a point P at (3, 2) is translated by the vector (4, -1), what are the coordinates of the new point P'?

Answer: 7, 1

Question 2: Translate the point A(5, -3) using the vector (-2, 4). What are the coordinates of the translated point?

Answer: 3, 1

Question 3: Construct the image of the point (2, 4) after applying the translation vector (3, -2).

Answer: 5, 2

Question 4: A point B is at (0, 0). If it is translated by the vector (x, y) and ends up at (5, 3), find the values of x and y.

Answer: x=5, y=3

Question 5: A rectangle has vertices at (1, 2), (4, 2), (4, 5), and (1, 5). If all points are translated by the vector (2, -3), what are the new coordinates of the vertices?

Answer: 3, -1; 6, -1; 6, 2; 3, 2

Question 6: Explain why translating a point using a vector preserves the shape and size of a figure.

Answer: Translation moves all points equally without changing distances or angles, thus preserving the shape and size.

Question 7: A triangle has vertices at (2, 3), (4, 5), and (3, 7). If it is translated by the vector (-2, 2), what are the new coordinates of the vertices?

Answer: 0, 5; 2, 7; 1, 9

Question 8: Construct a translation that moves the point (6, 4) to the point (2, 1). What is the translation vector?

Answer: -4, -3

Question 9: Identify the common mistake made when translating points, and explain how to correct it.

Answer: A common mistake is adding instead of subtracting the vector components when the signs are negative. To correct it, students should carefully check the signs and perform the correct addition or subtraction.

Question 10: For the point (–1, 3), apply the translation vector (4, 5). What are the new coordinates?

Answer: 3, 8

Question 11: A school bus starts at (0, 0) and moves according to the vector (3, 4). Where will the bus be after 5 moves?

Answer: 15, 20