Let's consider the transformations one by one on the given ordered pair [tex]\((1, -3)\)[/tex]:
1. Reflection across the y-axis:
- To reflect a point across the y-axis, we take the point [tex]\((x, y)\)[/tex] and transform it to [tex]\((-x, y)\)[/tex].
- Therefore, reflecting [tex]\((1, -3)\)[/tex] across the y-axis results in:
[tex]\[
(-1, -3)
\][/tex]
2. Dilation with a scale factor of 2:
- To dilate a point by a scale factor of 2, we multiply both the [tex]\(x\)[/tex] and [tex]\(y\)[/tex] coordinates by 2.
- Applying this dilation to the reflected point [tex]\((-1, -3)\)[/tex] results in:
[tex]\[
(2 \times -1, 2 \times -3) = (-2, -6)
\][/tex]
After performing these transformations, the coordinates of the transformed image are [tex]\((-2, -6)\)[/tex].
Therefore, the ordered pairs after each transformation step are:
1. After reflection across the y-axis: [tex]\((-1, -3)\)[/tex]
2. After dilation by a scale factor of 2: [tex]\((-2, -6)\)[/tex]
