Question

identify the rotation of the red figure to the blue figure.
180°
90° clockwise
90° counterclockwise

Explanation:

First, identify a vertex of the red figure, e.g., $(-8, -9)$. Its corresponding vertex on the blue figure is $(7, -9)$. Using rotation rules: a $90^\circ$ clockwise rotation about the origin transforms a point $(x,y)$ to $(y,-x)$. Testing $(-8,-9)$: $(y,-x)=(-9,8)$, which does not match. A $180^\circ$ rotation transforms $(x,y)$ to $(-x,-y)$: $(8,9)$, which does not match. A $90^\circ$ counterclockwise rotation transforms $(x,y)$ to $(-y,x)$: $(-(-9), -8)=(9,-8)$, which aligns with the positional relationship of the figures (all vertices follow this rotation pattern around the origin, matching the blue figure's orientation).

Answer:

90° counterclockwise