Question

answer
a rotation of 90° clockwise about the origin
a reflection over the line x = 4
a rotation of 180° clockwise about the origin
a reflection over the line y = 5

Explanation:

Step1: Recall rotation and reflection rules

For a 90 - degree clock - wise rotation about the origin, the transformation rule for a point $(x,y)$ is $(y, - x)$. For a 180 - degree clock - wise rotation about the origin, the rule for a point $(x,y)$ is $(-x,-y)$. For a reflection over the line $x = a$, the rule for a point $(x,y)$ is $(2a - x,y)$ and for a reflection over the line $y = b$, the rule for a point $(x,y)$ is $(x,2b - y)$.

Step2: Analyze the given square's position

Let's assume a general point on the original square. Without knowing the exact pre - image and image points, we can use the properties of the transformations. A 90 - degree clock - wise rotation about the origin would change the orientation of the square in a particular way. A 180 - degree clock - wise rotation about the origin would flip the square to the opposite side of the origin. A reflection over $x = 4$ would move the square to the other side of the vertical line $x = 4$. A reflection over $y = 5$ would move the square to the other side of the horizontal line $y = 5$.

Step3: Check the rotation and reflection effects

If we consider the symmetry and position of the square with respect to the origin and the given lines. A 180 - degree clock - wise rotation about the origin would map the square to a position that is opposite to its original position with respect to the origin.

Answer:

a rotation of 180° clockwise about the origin