Question 1: Express the translation of point P(3, 5) to point Q using the vector notation (a, b).

Answer: [a=, b=]

Question 2: If the translation vector is (4, -2), what are the coordinates of the translated point of R(7, 3)?

Answer: [x=, y=]

Question 3: Construct the translation vector that moves point A(2, 3) to point B(5, 7).

Answer: [a=3, b=4]

Question 4: Plot the translation vector (2, -3) starting from point C(6, 4).

Answer: New point at (8, 1)

Question 5: Translate point D(0, 0) by vector (−5, 6). What are the new coordinates?

Answer: [x=−5, y=6]

Question 6: A translation is represented as T: (x, y) → (x + a, y + b). If a point P is translated to P', write the notation showing the original point and the translated point.

Answer: P(x, y) → P'(x + a, y + b)

Question 7: Given vector (−2, 3), what is the notation for translating a point Q(4, 5)?

Answer: Q'(4−2, 5+3) or Q'(2, 8)

Question 8: A point P(−1, 4) is translated by vector (3, 2). Write the translation notation and find the new point.

Answer: P'(2, 6)

Question 9: In a real-world scenario, a delivery truck moves from location (10, 20) to (15, 25). Write the translation vector and the notation for this movement.

Answer: Translation vector: (5, 5); Notation: (x, y) → (x + 5, y + 5)

Question 10: Identify and correct the mistake in the following notation: (x, y) → (x + b, y + a) when describing a translation.

Answer: The correct notation should be (x, y) → (x + a, y + b).

Question 11: Challenge: If a point P moves with translation vector (a, b) and then again with vector (c, d), express the resulting translation as a single vector.

Answer: [a+c, b+d]