Final answer:
To find M' after reflection across x=1, the x-coordinate of M changes to an equal distance on the opposite side of the axis, but not 1, and the y-coordinate remains the same. Option B is incorrect as it suggests that the x-coordinate did not change.
Step-by-step explanation:
To find the reflection of point M across the line x=1, any point (x, y) on the quadrilateral would be reflected to a new point where the x-coordinate would be changed to be the same distance away from the line x=1 but on the opposite side. The y-coordinate remains the same because the reflection is horizontal and does not affect the vertical position.
Suppose the original coordinates of M are (a, y), where a is unknown. Upon reflection, if 'a' is greater than 1, the reflected x-coordinate will be subtracted from 2. If 'a' is less than 1, it will be added to 2. Therefore the reflected x-coordinate cannot be 1 (As it must move), it will be a distance from 1 equal to but on the opposite side from its original distance to 1.
In general, the reflection of a point (a, y) across the line x = 1 can be found by using the formula x' = 2 - a. Therefore, since we don't have the exact x-coordinate of M, we cannot determine the exact new position, but we can infer that the x-coordinate of M' will not be 1 as the point must have either moved to the left or right of the axis x = 1. Based on this, option B is not the correct answer because it implies that the x-coordinate did not change, which is not possible for a reflection across x = 1. The correct answer will depend on whether the original x-coordinate was less than or greater than 1.