Answer:
Option C.
Step-by-step explanation:
Let a point (x, y) has a sequence of transformations,
Option A).
Reflects across x-axis then the coordinates will be,
(x, y) → (x, -y)
Then reflects across the y-axis,
(x, -y) → (-x, -y)
Image (x, y) gets changed to (-x, -y) therefore, point (x, y) doesn't map onto itself.
Option B).
(x, y) rotate 90° counter clockwise about the origin.
(x, y) → (-y, x)
Then reflect across x-axis,
(-y, x) → (y, x)
Since coordinates of the image and the actual are not same therefore, image doesn't map itself.
Option C).
(x, y) when reflected across x-axis,
(x, y) → (x, -y)
Then reflected over the x-axis,
(x, -y) → (x, y)
In this option point (x, y) maps onto itself after these transformations.
Option D).
(x, y) rotated 90°counterclockwise about the origin
(x, y) → (-y, x)
Then translated up by 2 units.
(-y, x) → (-y, x+2)
Therefore, (x, y) gets changed after these transformations and doesn't maps itself.
Option (C) will be the answer.
. So we can add twice the first equation to the second one to get
, we have 
so
, then
, then
