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Question

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.

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+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)

Answer 1

To find the sequence of transformations that will carry triangle \( \Delta ABC \) to triangle \( \Delta A"B"C" \), we need to describe the transformation that goes from the original coordinates to the transformed coordinates.

1. Reflection Over the x-axis: The first transformation is a reflection over the x-axis. This changes the coordinates from \((x, y)\) to \((x, -y)\).

2. Translation Upward: The second transformation is a vertical translation. Since the triangle appears to move upward, the transformation will add 4 to the y-coordinate. This takes the form of \((x, -y) \rightarrow (x, -y + 4)\).

Combining these transformations, we have:

• Start: \((x, y)\)
• Reflection: \((x, y) \rightarrow (x, -y)\)
• Translation: \((x, -y) \rightarrow (x, -y + 4)\)

Thus, the complete transformation is: \[ (x, y) \rightarrow (x, -y + 4) \]

The answer is: (x,y)→(x,−y+4).