what is the image of A(3-1) after a reflection first across the line y=3 and then across the line x=-1
To find the image of point A(3, -1) after a reflection across the line y=3, we need to reflect it directly across y=3:
In this case, the x-coordinate remains the same, and the y-coordinate changes sign.
The image of A(3, -1) after the first reflection is A(3, 5).
Now, to reflect the point A(3, 5) across the line x=-1, we need to reflect it directly across x=-1:
In this case, the y-coordinate remains the same, and the x-coordinate changes sign.
The image of A(3, 5) after the second reflection is A(-3, 5).
Therefore, the image of A(3, -1) after a reflection first across the line y=3 and then across the line x=-1 is A(-3, 5).