what is the image of a(3 -1) after a reflection, first across the line y=3, then across the line x=-1
(-5,7)
(3,-1)
(-5,-1)
(-1,-5)
(3,-1) is 4 below y=3, so its reflection will be to 4 above y=3, or (3,7)
Similarly for x=-1, to (-5,7)
To find the image of a point after a reflection, you need to follow these steps:
1. Find the reflection of the point across the line y=3:
To reflect a point across a horizontal line like y=3, you keep the x-coordinate the same, but change the sign of the y-coordinate. In this case, the point (3, -1) reflects to (3, 5).
2. Find the reflection of the new point across the line x=-1:
To reflect a point across a vertical line like x=-1, you keep the y-coordinate the same, but change the sign of the x-coordinate. In this case, the point (3, 5) reflects to (-3, 5).
Therefore, the image of the point (3, -1) after a reflection across the line y=3, and then across the line x=-1, is (-3, 5).
None of the answer choices match this result.