Final answer:
The coordinates of point M are d) (-2, 6). This is found by determining the distance point L is from the center in both x and y directions and reflecting that distance across the center to find point M.
Step-by-step explanation:
The coordinates of point M on the circle can be determined using the fact that LM is a diameter of the circle and the coordinates of the center and point L.
Since the center of the circle is at (-5, 0) and point L is at (-8, 6), we can find the midpoint of LM which should be the center of the circle (since the diameter crosses through the center). However, given that we already know the center, we can instead find the coordinates of point M by considering that the change in x and y from L to the center is the same from the center to M but in the opposite direction.
The change in x from point L to the center is -5 - (-8) = 3, so the x-coordinate of M will be -5 - 3 = -2.
The change in y from point L to the center is 0 - 6 = -6, so the y-coordinate of M will also be 0 - (-6) = 6.
Therefore, the coordinates of M are (-2, 6).