Question

which diagram shows δuvw rotated 90° counterclockwise about w?

Explanation:

Step1: Recall rotation rule

A 90° counterclockwise rotation about a point $(x,y)$ transforms a point $(a,b)$ to $(x-(b-y), y+(a-x))$. For center $W$, $W$ stays fixed.

Step2: Check rotation direction

Counterclockwise rotation of $\Delta UVW$ about $W$ should turn segments $WU$ and $WV$ 90° left around $W$. The top diagram shows green $\Delta U'V'W$ with $WU'$ and $WV'$ in the correct counterclockwise orientation relative to $WU$ and $WV$.

Step3: Verify fixed point

$W$ is the center, so it is shared between the original and rotated triangles in both diagrams, but only the top diagram matches the 90° counterclockwise direction.

Answer:

The Top Diagram