Question

answer
a reflection over the line y = x
a rotation of 180° clockwise about the origin
a reflection over the line x = - 2
a reflection over the line y = -x

Explanation:

Step1: Recall transformation rules

For a reflection over $y = x$, the rule is $(x,y)\to(y,x)$. For a $180^{\circ}$ clock - wise rotation about the origin, the rule is $(x,y)\to(-x,-y)$. For a reflection over $x = a$, the rule is $(x,y)\to(2a - x,y)$. For a reflection over $y=-x$, the rule is $(x,y)\to(-y,-x)$.

Step2: Analyze the figure

We can pick a point on the original figure and its corresponding point on the transformed figure. Let's assume a point $(x_1,y_1)$ on the original figure and its image $(x_2,y_2)$ on the new figure. By observing the orientation and position of the figure, if we consider a point $(x,y)$ on the original figure and see that its image is $(-y,-x)$ after the transformation. This follows the rule of reflection over the line $y=-x$.

Answer:

a reflection over the line $y = -x$