Question

The composition transformation is a reflection over the y-axis followed by the translation.

Answer 1

To describe the composition transformation that consists of a reflection over the y-axis followed by a translation, let's break it down into two steps:

1. **Reflection over the y-axis**: This transformation takes a point \((x, y)\) and maps it to \((-x, y)\). This means that the x-coordinate changes sign while the y-coordinate remains the same.

2. **Translation**: A translation moves each point of the shape by a fixed distance in a specified direction. For instance, translating a point \((x, y)\) by \(a\) units in the x-direction and \(b\) units in the y-direction results in the point \((x + a, y + b)\).

Now, combining these two transformations:

- Start with a point \((x, y)\).
- Reflect it over the y-axis:
\[
(-x, y)
\]
- Next, apply the translation. Assuming the translation moves the point by \(a\) units horizontally and \(b\) units vertically, we then have:
\[
(-x + a, y + b)
\]

Thus, the overall transformation can be expressed in one step:
\[
(x, y) \to (-x + a, y + b)
\]

In summary, a composition of a reflection over the y-axis and then a translation results in the transformation:
\[
T(x, y) = (-x + a, y + b)
\]