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)

Answer 1

To determine the sequence of rigid transformations that map quadrilateral ABCD to A"B"C"D", we need to carefully analyze the transformations given and their effects on the coordinate points.

1. **Reflection**: The transformation (x,y) → (−x,y) reflects the points across the y-axis. If the original shape ABCD is positioned in the standard orientation, this reflection can invert its x-coordinates.

2. **Translation**: After reflection, we may need to adjust the position of the shape. The transformation (x,y) → (x,y−4) translates the shape down by 4 units on the y-axis.

In combination, the transformations can be represented as:

- First, reflect: (x,y) → (−x,y) (reflection across the y-axis)
- Then, translate: (−x,y) → (−x,y−4) (translation downward by 4)

Combining these transformations leads us to the final composite transformation mapping:

**Composition of Transformations**:

1. Reflect across the y-axis: \( (x,y) \rightarrow (-x,y) \)
2. Translate downwards: \( (-x,y) \rightarrow (-x,y-4) \)

Thus, the sequence of transformations is:

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

Having analyzed the transformations, if we need to select the correct transformation from your options, the closest fit for this composition would be:

**(x,y)→(−x,y−4)**

This matches the transformation sequence needed to map ABCD to A"B"C"D".