Answer:
Option (4).
Step-by-step explanation:
Let's take the coordinates of point A for the set of reflections and rotations given in the options.
Option (1). Rotate 180° → A(-4, 1) becomes (4, -1)
Reflect over x-axis → (4, -1) becomes (4, 1)
Reflect over the line y = x → (4, 1) becomes A'(1, 4)
Therefore, point A will not overlap itself after the number of transformations given.
Option (2). Reflect across x-axis → A(-4, 1) will become (-4, -1)
Rotate 180° → (-4, -1) becomes (4, 1)
Reflect over the x-axis → (4, 1) becomes A'(4, -1)
Therefore, point A(-4, 1) doesn't overlap A'(4, -1).
Option (3). Rotate 180° → A(4, 1) becomes (-4, -1)
Reflect over the y-axis → (-4, -1) becomes (4, -1)
Reflected over y = x → (4, -1) becomes (-1, 4)
So the point A(4, 1) becomes A'(-1, 4) after the set of reflections,
Option (4). Reflect over the y axis → A(-4, 1) becomes (4, 1)
Reflect over the x-axis → (4, 1) becomes (4, -1)
Rotate 180° → (4, -1) becomes A'(-4, 1)
Therefore, point A will overlap itself following the set of transformations.
