Question

Which sequence of transformations maps ∆ABC to ∆A”B”C”? * 3 points A. a reflection over the y-axis followed by (x, y) → (x + 3, y + 7) B. a reflection over the x-axis followed by (x, y) → (x + 7, y + 3) C. (x, y) → (x – 3, y – 7) followed by a reflection over the x-axis D. (x, y) → (x – 3, y – 7) followed by a reflection over the y-axis

Answer 1

The correct answer is B. a reflection over the x-axis followed by (x, y) → (x + 7, y + 3).

To transform ∆ABC to ∆A”B”C”, we need to consider the following steps:

Horizontal Shift: ∆ABC is shifted 3 units to the right, which can be achieved by the transformation (x, y) → (x + 3, y).

Vertical Shift: ∆ABC is shifted 7 units downward, which can be achieved by the transformation (x, y) → (x, y - 7).

Reflection over the x-axis: Since ∆A”B”C” is reflected across the x-axis, we need to negate the y-coordinate. This can be achieved by the transformation (x, y) → (x, -y).

Combining these transformations, we get the sequence:

(x, y) → (x + 3, y) → (x, y - 7) → (x, -y)

Therefore, the correct answer is B. a reflection over the x-axis followed by (x, y) → (x + 7, y + 3).