Let's analyze the given transformations step-by-step for the point [tex]\(X\)[/tex] with coordinates [tex]\((-3, 10)\)[/tex].
### Step 1: Translation
The translation rule given is [tex]\((x, y) \rightarrow (x+5, y-3)\)[/tex].
Applying the translation to [tex]\(X\)[/tex]:
[tex]\[
x' = -3 + 5 = 2
\][/tex]
[tex]\[
y' = 10 - 3 = 7
\][/tex]
So, after the translation, the coordinates of [tex]\(X\)[/tex] are [tex]\((2, 7)\)[/tex].
### Step 2: Rotation
The rotation rule for a [tex]\(90^\circ\)[/tex] clockwise rotation is [tex]\((x, y) \rightarrow (y, -x)\)[/tex].
Applying the rotation to the translated coordinates [tex]\((2, 7)\)[/tex]:
[tex]\[
x'' = y' = 7
\][/tex]
[tex]\[
y'' = -x' = -2
\][/tex]
So, after the rotation, the coordinates of [tex]\(X\)[/tex] are [tex]\((7, -2)\)[/tex].
### Conclusion
The location of [tex]\(X'\)[/tex] after translating the point [tex]\((-3, 10)\)[/tex] using the rule [tex]\((x, y) \rightarrow (x+5, y-3)\)[/tex] and then rotating the point [tex]\(90^\circ\)[/tex] clockwise is [tex]\((7, -2)\)[/tex].
Thus, the correct answer is not listed among the provided options exactly, but analyzing the given details, the closest matching step appears to be:
[tex]\[
(7, -2)
\][/tex]
Which is not in the provided options—seems like there is a discrepancy or error in problem statement options.
Therefore, please reach out for further clarification or correction in the options provided.
