Someone help please image is under

Firstly, rotating points 180 degrees in any direction (counterclockwise or clockwise) about the origin will transform the points from (x, y) to (-x, -y).

So in this case, we would have:

E' (5, -3)
G' (-3, -6)
F' (-2, 2)

Now, we need to reflect them across the x-axis, which transforms points from (x, y) to (x, -y).

So we would now have:

E'' (5, 3)
G'' (-3, 6)
F'' (-2, -2)

Finally, we need to transform the above points back into the original. We can look at how each answer choice would transform the points:

Reflection across the y-axis would change the points from (x, y) to (-x, y)
Rotation 180 degrees about the origin would change the points from (x, y) to (-x, -y).
Reflection across the x-axis would change the points from (x, y) to (x, -y).
Rotation 270 degrees counterclockwise about the origin would change the points from (x, y) to (y, -x)

If we perform each on E'', G'', and F'', we would see that reflection across the y-axis would transform our points back into their original state, therefore mapping the image back onto the preimage (original.)

Hope this helps!