Final answer:
The coordinates of point L after a 90° rotation about the origin and the translation (x, y) → (x - 8, x + 5) are (-5, 8). However, since this final coordinate does not match the given options, there seems to be an error or misunderstanding in the application of the transformations to the provided options.
Step-by-step explanation:
To find the final coordinates of point L after a 90° rotation about the origin followed by a translation, first apply the rotation. A 90° rotation about the origin means that the point (x, y) will become (-y, x). Once we have these new coordinates, we can then apply the translation rule (x, y) → (x - 8, x + 5) to find the final position.
Let's assume the original coordinates of point L are (Lx, Ly). After rotating 90°, the new coordinates will be (-Ly, Lx). Now apply the translation: (-Ly - 8, Lx + 5).
Since the original coordinates of point L are not given, we cannot determine the final exact coordinates. However, the student is asked to choose from given options A, B, C, or D, implying the translation is to be applied on the results of the rotation directly provided in the options, rather than on the original coordinates of L.
If we consider an option such as (-3, 8) and apply the translation, the point would translate to (-3 - 8, -3 + 5) = (-11, 2), which doesn't match any given choices. Hence, the correct final coordinates can be found by applying the translation to each option and choosing the one that fulfills the condition that the y component after the translation becomes the x component after the rotation plus 5.
By applying this process option B (3, -8) becomes (3 - 8, 3 + 5) = (-5, 8), which correctly corresponds to rotating (8, 3) by 90° (becomes (-3, 8)) and then applying the translation to the rotated coordinates.