Question

Coordinates of point A after reflection over the x-axis and then reflecting that point over the line x = 1:

A) (1,1)
B) (-1,-1)
C) (1,-1)
D) (-1,1)

Answer 1

The coordinates of point A after reflection over the x-axis and then reflecting that point over the line x = 1 remain (1,-1).

Step-by-step explanation:

The subject of this schoolwork question is Mathematics, specifically dealing with coordinate transformations in the context of reflections. The initial point is A, and the student is asked to determine the coordinates of point A after two specific transformations:

1. Reflection over the x-axis
2. Reflection over the line x = 1

To perform these transformations step by step for point A with coordinates (1,1):

1. The first transformation reflects point A over the x-axis, which changes the sign of the y-coordinate but leaves the x-coordinate unchanged, resulting in new coordinates (1,-1).
2. The second transformation reflects this new point over the line x=1. To reflect over the line x=1, we calculate how far point A is from the line x=1 (which is 0 units in this case), and then move the point that same distance in the positive x direction of the coordinate system, keeping it at (1, -1).

Therefore, after these transformations, the coordinates of point A remain (1,-1).