Question

Use the image to answer the question. Identify the sequence of transformations that will carry ΔABC→ΔA"B"C". Give your answer in the form of a composition transformation mapping. (1 point) Responses (x,y)→(x,−y−4) open paren x comma y close paren rightarrow open paren x comma negative y minus 4 close paren (x,y)→(x−4,−y) left parenthesis x comma y right parenthesis right arrow left parenthesis x minus 4 comma negative y right parenthesis (x,y)→(x+4,−y) left parenthesis x comma y right parenthesis right arrow left parenthesis x plus 4 comma negative y right parenthesis (x,y)→(x,−y+4)

Answer 1

To determine the sequence of transformations that maps ΔABC to ΔA"B"C", we need to analyze the transformation steps.

1. **Reflect** over the x-axis: This transformation changes the coordinates from \((x, y)\) to \((x, -y)\).

2. **Translate** downward by 4 units: After reflecting, we would move the points down by 4 units. This is achieved by changing the y-coordinate, resulting in \((x, -y) \to (x, -y - 4)\).

Therefore, the composition of these transformations is:

1. **Reflection**: \((x, y) \to (x, -y)\)
2. **Translation**: \((x, -y) \to (x, -y - 4)\)

Combining these two transformations can be written as:

\[
(x, y) \to (x, -y) \to (x, -y - 4)
\]

Therefore, the final transformation that maps ΔABC to ΔA"B"C" is:

\[
(x, y) \to (x, -y - 4)
\]

Hence, the correct answer is:

\((x,y) \to (x, -y - 4)\).