Final answer:
The glide reflection described involves a translation by a vector of (-6, -2) from point M to M', but the axis of reflection cannot be determined from the information given.
Step-by-step explanation:
The glide reflection that has been described in the question involves the translation of point M with coordinates (4, 8) to its image M' with coordinates (-2, 6). A glide reflection combines two actions: a translation and a reflection. To find the translation component, we need to look at the change in the x and y coordinates separately.
For the x-coordinate, we go from 4 to -2, which is a change of -6 units (to the left, since it's negative). For the y-coordinate, we go from 8 to 6, which is a change of -2 units (downwards, since it's negative). Now, combining these changes, we have a translation vector of (-6, -2).
After the translation, a reflection would occur to account for any orientation change in the point's image. However, from the given information, we cannot definitively determine the axis of reflection, but it might very well be a vertical or horizontal line, or even a slant line, depending on the context not provided here.