Question

answer
a reflection over the line y = -x - 9
a reflection over the line x = 5
a rotation of 90° clockwise about the origin
a rotation of 180° counterclockwise about the origin

Explanation:

Step1: Recall transformation rules

For a reflection over the line $y=-x - 9$, we use the general formula for reflection over a line $y = mx + c$. For a reflection over the line $x = 5$, points $(x,y)$ transform to $(10 - x,y)$. For a $90^{\circ}$ clock - wise rotation about the origin, the transformation rule is $(x,y)\to(y,-x)$. For a $180^{\circ}$ counter - clockwise rotation about the origin, the transformation rule is $(x,y)\to(-x,-y)$.

Step2: Analyze the figure

The figure appears to be symmetric about the origin. If we take a point $(x,y)$ on the original figure and its corresponding point on the other side of the origin, the relationship is $(x,y)\to(-x,-y)$. This is the rule for a $180^{\circ}$ counter - clockwise rotation about the origin.

Answer:

a rotation of $180^{\circ}$ counterclockwise about the origin