Question

Compositions of Transformations Quick Check 4 of 54 of 5 Items Question Use the image to answer the question. Identify a sequence of rigid transformations that would map ABCD→A"B"C"D" . 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 negative x minus 4 comma y right parenthesis (x,y)→(−x,y−4) left parenthesis x comma y right parenthesis right arrow left parenthesis negative x comma y minus 4 right parenthesis (x,y)→(x,y+4) left parenthesis x comma y right parenthesis right arrow left parenthesis x comma y plus 4 right parenthesis (x,y)→(x,−y−4) left parenthesis x comma y right parenthesis right arrow left parenthesis x comma minus y negative 4 right parenthesis Skip to navigation page 14 of 14 Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.Formula keypad has been closed. Press Control + Backslash to open it again.

Answer 1

To determine the sequence of rigid transformations that maps triangle ABCD to triangle A"B"C"D", we need to identify the transformations needed, which could include translations, reflections, and rotations.

1. **Reflection**: If we reflect across the y-axis, the transformation would change the coordinates of any point \( (x, y) \) to \( (-x, y) \).

2. **Translation**: After reflection, we may need to translate the transformed figure. For example, if we want to move the figure 4 units to the left, the transformation would change the coordinates to \( (-x - 4, y) \).

Therefore, the composition of transformations that would map ABCD to A"B"C"D" can be described as:
1. Reflect across the y-axis: \( (x, y) \rightarrow (-x, y) \)
2. Translate left by 4 units: \( (-x, y) \rightarrow (-x - 4, y) \)

The overall transformation can be written as:
\[
(x, y) \rightarrow (-x - 4, y)
\]

This matches the first option given in the responses:
- \((x,y) \rightarrow (-x - 4, y)\)

Thus, the correct answer is:
\[
\textbf{(x,y)→(−x−4,y)}
\]