Question 1: Write the translation vector of point P(3, 5) moving 4 units right and 2 units down using correct notation.

Answer: → egin{bmatrix} 4 \ -2 \\ end{bmatrix}

Question 2: Identify the error in the following vector notation: v = (3, -4).

Answer: Incorrect notation; should use brackets and arrow: v = [→ egin{bmatrix} 3 \ -4 \\ end{bmatrix}

Question 3: Construct the translation vector for moving a point from (1, 2) to (4, 5).

Answer: → egin{bmatrix} 3 \ 3 \\ end{bmatrix}

Question 4: Explain why the notation [→ egin{bmatrix} x \ y \\ end{bmatrix} is preferred over (x, y) for vectors.

Answer: Because the notation with brackets and the arrow clearly indicates a vector, distinguishing it from a point or coordinate pair.

Question 5: A translation moves point A(2, 3) to point B(5, 7). Write the translation vector, ensuring correct notation.

Answer: → egin{bmatrix} 3 \ 4 \\ end{bmatrix}

Question 6: Identify the mistake in this vector notation used in a student's work: v = [3, 4].

Answer: Incorrect; should use brackets and arrow: v = [→ egin{bmatrix} 3 \ 4 \\ end{bmatrix}

Question 7: Plot the translation vector [→ egin{bmatrix} -2 \ 5 \\ end{bmatrix} on the grid.

Answer: Student draws vector pointing 2 units left and 5 units up from the origin.

Question 8: A student writes [→ (4, -3)] when asked for a translation vector. Correct this notation.

Answer: Use brackets and arrow: [→ egin{bmatrix} 4 \ -3 \\ end{bmatrix}

Question 9: Given the vector [→ egin{bmatrix} 1 \ -2 \\ end{bmatrix}, identify if the notation is correct. If not, correct it.

Answer: Correct notation.

Question 10: Explain the importance of consistent vector notation when communicating translation moves in geometry.

Answer: Consistent notation ensures clarity, prevents confusion with points vs. vectors, and allows accurate communication of translation operations.

Question 11: A student writes a translation vector as (5, 2) but intends to show a vector. Identify and correct the mistake.

Answer: Should use brackets and arrow: [→ egin{bmatrix} 5 \ 2 \\ end{bmatrix}