Question

Which composition transformation occurs in the following? (x,y) (y +5, -x)
a reflection across the x-axis and a translation to the left by -5
A 180-degree rotation and a translation to the right by 5
A 90-degree clockwise rotation and a translation to the right by 5
a reflection across the y-axis and a translation to the right by 5

Answer 1

To determine the composition transformation represented by the transformation \((x,y) \to (y + 5, -x)\), let's break it down step by step:

1. **Identify the components of the transformation:**
- The resulting point is \((y + 5, -x)\).
- The first component, \(y + 5\), indicates a transformation related to the y-coordinate.
- The second component, \(-x\), indicates a transformation related to the x-coordinate.

2. **Analyze the transformations:**
- The transformation of \(-x\) corresponds to a reflection across the y-axis, as it flips the x-coordinate.
- The transformation of \(y + 5\) corresponds to a vertical translation (translation up) by 5 units.

3. **Combine the observations:**
- First, the original point \((x, y)\) undergoes a reflection across the y-axis, which changes \((x, y)\) to \((-x, y)\).
- Then, it translates this result up by adding 5 to the y-coordinate, changing it from \((-x, y)\) to \((-x, y + 5)\).

### Conclusion:
The full transformation \((x,y) \to (y + 5, -x)\) corresponds to a reflection across the y-axis followed by a translation upwards by 5.

However, since none of the options given fully matches this description, if we assume "right by 5" was intended to be "up by 5," the answer would be similar to one of the given options.

**Correct Transformation Description**: Reflection across the y-axis and an upward translation (by +5) of the y-coordinate.

Since the options provide no only vertical translations and misrepresent the transformation in strict terms, it is hard to pick the closest fitting option. Based on your descriptions, it is essential to check if "up" or "down" is intended over simple horizontal translations. If adjusting for that, please specify if the choice was only about orientation modifications strictly!