Question 1: Write the translation vector for moving point P(2, 3) by the vector (4, -1). Use proper notation.

Answer: T = (4, -1)

Question 2: If a point Q(5, -2) is translated by the vector (3, 4), what are its new coordinates?

Answer: Q' = (8, 2)

Question 3: Express the translation of point R(0, 0) by vector (−2, 5) using vector notation.

Answer: T = (−2, 5)

Question 4: Construct a translation on the grid that moves point A(1, 1) to point B(4, 5). What is the translation vector?

Answer: T = (3, 4)

Question 5: Translate point C(−3, 2) using the vector (2, −3). Write the notation for this translation.

Answer: T = (2, -3)

Question 6: A point S has coordinates (7, -4). If it is translated by the vector (−1, 3), what are the new coordinates? Show your working.

Answer: S' = (6, -1)

Question 7: Identify the error in the following translation notation: T = (−2, 5) moves point (3, 4) to (1, 9). Is this correct? Explain.

Answer: No, because (3 + (−2), 4 + 5) = (1, 9) is correct. The notation is correct.

Question 8: Express the translation that moves point (−1, 2) to (2, 5) using vector notation. Show your reasoning.

Answer: T = (3, 3)

Question 9: Given the translation vector T = (4, -2), what is the translation of point (0, 0)? Write the result in coordinates.

Answer: New point: (4, -2)

Question 10: For the vector notation T = (x, y), explain what each part represents in terms of translation movement.

Answer: x and y represent the horizontal and vertical components of the translation, respectively.

Question 11: Identify and correct the mistake in this translation: T = (−3, 4) moves point (1, 2) to (−2, 6). Is the move correct?

Answer: Yes, because (1 + (−3), 2 + 4) = (−2, 6). The notation is correct.