Question

answer
a reflection over the line y = x
a counterclockwise rotation of 180° about the origin
a counterclockwise rotation of 270° about the origin
a reflection over the line y = -x

Explanation:

Step1: Recall transformation rules

For a point $(x,y)$ reflected over $y = x$, it becomes $(y,x)$; for a $180^{\circ}$ counter - clockwise rotation about the origin, $(x,y)$ becomes $(-x,-y)$; for a $270^{\circ}$ counter - clockwise rotation about the origin, $(x,y)$ becomes $(y, - x)$; for a reflection over $y=-x$, $(x,y)$ becomes $(-y,-x)$.

Step2: Analyze the transformation

Let's take a general point on figure A and see its transformation to figure B. If we consider a point $(x,y)$ on figure A and observe its corresponding point on figure B. A $270^{\circ}$ counter - clockwise rotation about the origin maps a point $(x,y)$ to $(y,-x)$. By checking the coordinates of the vertices of figure A and figure B, we can see that this is the correct transformation.

Answer:

A counterclockwise rotation of 270° about the origin