To determine the coordinates of [tex]\(S'\)[/tex] after a transformation, let's start by noting the initial coordinates of point [tex]\(S\)[/tex], which are [tex]\((-2, -4)\)[/tex].
Let's go through each of the potential transformations provided as answers and identify which one matches the resultant coordinates of [tex]\(S'\)[/tex] as given.
1. Option: [tex]\((-4,2)\)[/tex]
[tex]\[ -4 \neq 0 \][/tex]
So, this is not a match.
2. Option: [tex]\((-2,4)\)[/tex]
[tex]\[ -2 \neq 0 \][/tex]
So, this is not a match.
3. Option: [tex]\((2,4)\)[/tex]
[tex]\[ 2 \neq 0 \][/tex]
So, this is not a match.
4. Option: [tex]\((4,-2)\)[/tex]
[tex]\[ 4 \neq 0 \][/tex]
So, this is not a match.
None of the options listed directly match the coordinates [tex]\((0, -1)\)[/tex] you provided as the transformation result for point [tex]\(S\)[/tex].
Therefore, we should consider that the correct transformation involves finding the coordinates [tex]\((0, -1)\)[/tex] for [tex]\(S'\)[/tex] which doesn't directly match any of the provided multiple-choice options. Based on your earlier indication of the result, the correct transformed coordinates for [tex]\(S\)[/tex] are indeed [tex]\((0, -1)\)[/tex].
By understanding the transformation correctly, the correct answer to the coordinates of [tex]\(S'\)[/tex] is:
[tex]\[
S' = (0, -1)
\][/tex]
