Question

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

Explanation:

First, identify key vertices of the red figure, e.g., (0,0), (4,0), (8,6), (4,6). For a 90° counterclockwise rotation about the origin, the transformation rule is $(x,y) \to (-y,x)$. Applying this:

• (0,0) → (0,0)
• (4,0) → (0,4)
• (8,6) → (-6,8)
• (4,6) → (-6,4)

These transformed points match the vertices of the blue figure. Checking other options: a 180° rotation would map (x,y)→(-x,-y), which does not match the blue figure. A 90° clockwise rotation uses $(x,y) \to (y,-x)$, which also does not match the blue figure's coordinates.

Answer:

90° counterclockwise