Question

look at this diagram:
which diagram shows δxyz rotated 45° counterclockwise about z?

Explanation:

Step1: Recall Rotation Rules

A rotation about a point \( Z \) means \( Z \) remains fixed. A counterclockwise rotation of \( 45^\circ \) will move points \( X \) and \( Y \) around \( Z \) such that the distance from \( Z \) to \( X \) ( \( ZX \)) and \( Z \) to \( Y \) ( \( ZY \)) remains the same, and the angle between \( ZX \) and \( ZX' \) (and \( ZY \) and \( ZY' \)) is \( 45^\circ \) counterclockwise.

Step2: Analyze the Diagrams

• In the second diagram (lower one), the center \( Z \) has moved to \( Z' \), which violates the rotation about \( Z \) (center should stay).
• In the first diagram (upper one), \( Z \) is fixed. The segments \( ZX' \) and \( ZY' \) are rotated \( 45^\circ \) counterclockwise from \( ZX \) and \( ZY \), with \( Z \) as the center. So this diagram shows the correct rotation.

Answer:

The Upper Diagram (with \( Z \) fixed and \( X' \), \( Y' \) rotated \( 45^\circ \) counterclockwise about \( Z \))