Answer: D. reflection across the line y = -x
Step-by-step explanation
When a rotation of 180º about the origin either in the clockwise or counterclockwise direction is made, the coordinates (x, y) changes to (-x, -y).
Considering the coordinates given are:
• A(3, 3)
,
• B(3, 5)
,
• C(1, 3)
Then if a rotation of 180º about the origin either in the clockwise or counterclockwise direction is made, the new coordinate:
• A'(-3, -3)
,
• B'(-3, -5)
,
• C'(-1, -3)
As we can see, either a rotation of 180º about the origin either in the clockwise or counterclockwise direction could have happened to the function. Thus, we are left with the rotations.
After reflection over the origin, the mirror image is formed in the opposite direction, meaning that (x, y) becomes (–x, –y), obtaining the same coordinates for A', B', and C' as before.
Finally, a reflection across the line y = -x switches the x and y-coordinates of all the points in a figure such that (x, y) becomes (-y, -x). Then, if this were true, the new coordinates would be:
• A'(-3, -3)
,
• B'(-5, -3)
,
• C'(-3, -1)
As this is not true, then this is the option.