Question

Compositions of Transformations Quick Check 5 of 55 of 5 Items 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) left parenthesis x comma y right parenthesis right arrow left parenthesis x comma negative y plus 4 right parenthesis (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)

Answer 1

To identify the sequence of transformations that will carry triangle \( \Delta ABC \) to \( \Delta A"B"C" \), we can analyze the transformations involved.

The transformations involve a reflection and a translation. The correct transformation sequence is:

1. Reflect over the x-axis: This will change \( (x, y) \) to \( (x, -y) \).
2. Translate upwards: Depending on the final position, if we need to move up, it could be represented as \( (x, -y) \) to \( (x, -y + k) \) for some \( k \).

From your options, the transformation that matches the description of reflecting across the x-axis and then translating is:

1. Translation by 4 units upwards after reflection: \( (x, y) \rightarrow (x, -y) \) to start, then shift up by 4 units to get \( (x, -y + 4) \).

Therefore, the correct composition transformation mapping is:

\[ (x, y) \rightarrow (x, -y + 4) \]

This indicates that \( \Delta ABC \) is first reflected over the x-axis and then moved up by 4 units.