The coordinate notation that represents the series of rotations is (x, y) → (y, -x) → (-y, x).
The total rotation is 0°, so the figure is at the same position,
In Mathematics, a rotation is a type of transformation which moves every point of the object through a number of degrees around a given point, which can either be clockwise or counterclockwise (anti-clockwise) direction.
For instance, we would apply a rotation of 270 degrees counterclockwise about the origin to point A (1, 2);
(x, y) → (y, -x)
A (1, 2) → A' (2, -1)
By applying a rotation of 90° counterclockwise around the origin to the new point A', the coordinates of its image are as follows:
(x, y) → (-y, x)
A' (2, -1) → A" (-(-1), 2) = (1, 2).
In this context, the total rotation is given by;
Total rotation = 360° - (270° + 90°)
Total rotation = 0°
In conclusion, the figure would remain at the same position because the series of rotations has a total rotation of zero degrees.