A coordinate plane shows two triangles A B C and A double dash B double dash C double dash. Both the axes range from negative 6 to 6 in unit increments.

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+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)
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,−y+4)

Answer 1

To identify the sequence of transformations that will map triangle ΔABC to triangle ΔA"B"C", we need to analyze the transformations.

1. The transformation involves altering the x-coordinates and then flipping the y-coordinates.

2. The first transformation suggests moving the triangle horizontally. The triangle appears to be moved 4 units to the right (if the x-coordinates of the points on triangle A"B"C" are 4 units higher than those on triangle ABC).

3. The second transformation flips the triangle across the x-axis, which affects the y-coordinates (i.e., it takes the y-coordinates and negates them).

Thus, the combination of these two transformations can be written as:

1. Translate right 4 units: \( f(x, y) = (x + 4, y) \)
2. Reflect over the x-axis: \( g(x, y) = (x, -y) \)

Putting it together, we have:

1. First transform: \( (x, y) → (x + 4, y) \)
2. Second transform: \( (x + 4, y) → (x + 4, -y) \)

So the overall transformation from \( ΔABC \) to \( ΔA"B"C" \) is:

\[ (x, y) → (x + 4, -y) \]

Thus, the correct answer is:

(x,y)→(x+4,−y)