Sure! Let's solve this step by step.
Given a pre-image point with coordinates [tex]\((3, -5)\)[/tex], we need to rotate this point [tex]\(90^{\circ}\)[/tex] clockwise.
To find the coordinates of a point rotated [tex]\(90^{\circ}\)[/tex] clockwise, we use the following transformation rule:
- The new [tex]\(x\)[/tex]-coordinate is given by the original [tex]\(y\)[/tex]-coordinate.
- The new [tex]\(y\)[/tex]-coordinate is given by the negation of the original [tex]\(x\)[/tex]-coordinate.
So, starting with the original point [tex]\((3, -5)\)[/tex]:
1. The original [tex]\(x\)[/tex]-coordinate is [tex]\(3\)[/tex].
2. The original [tex]\(y\)[/tex]-coordinate is [tex]\(-5\)[/tex].
Applying the transformation:
1. The new [tex]\(x\)[/tex]-coordinate will be the original [tex]\(y\)[/tex]-coordinate, which is [tex]\(-5\)[/tex].
2. The new [tex]\(y\)[/tex]-coordinate will be the negation of the original [tex]\(x\)[/tex]-coordinate, which is [tex]\(-3\)[/tex].
Thus, the coordinates of the image point after a [tex]\(90^{\circ}\)[/tex] clockwise rotation are [tex]\((-5, -3)\)[/tex].
Therefore, the correct answer is:
[tex]\[ (-5, -3) \][/tex]
