Final answer:
Reflecting the given points over x=-2 results in new coordinates that preserve the y-values. The correct image points after reflection are (-5,5), (-7,4), (-7,3), and (-5,1), which do not match any of the provided options.
Step-by-step explanation:
When reflecting a point over a vertical line such as x=-2, you find the horizontal distance of the point to the line and then map the point the same distance on the other side of the line. In this case, we are reflecting the pre-image points (1,5), (3,4), (3,3), and (1,1) over the line x=-2. To find the reflected points (image points), we calculate the horizontal distance from each pre-image point to the line and double it to determine how far the reflected point will be from the line, preserving the y-coordinates.
- The point (1,5) is 3 units away from -2. Doubling this, the reflected point is 3 units on the opposite side, which is at (-5,5).
- The point (3,4) is 5 units away from -2. Thus, the reflected point is at (-7,4).
- For (3,3), the horizontal distance is 5 units, and the reflected point is at (-7,3).
- Lastly, the point (1,1) is 3 units away, so the reflected point is at (-5,1).
None of the options provided in the question matches the correct answers. If the question intends the y-coordinates to be preserved after reflection, then the correct reflected coordinates are (-5,5), (-7,4), (-7,3), and (-5,1), which is not listed in the options provided.