Question

the graph of △abc is shown. which is different? a 90° counterclockwise rotation about the origin a 270° clockwise rotation about the origin a 90° leftward rotation about the origin a 270° counterclockwise rotation about the origin

Explanation:

Step1: Analyze rotation equivalence

A \(90^{\circ}\) counter - clockwise rotation about the origin is equivalent to a \(270^{\circ}\) clockwise rotation about the origin. Also, a \(90^{\circ}\) leftward rotation about the origin is the same as a \(90^{\circ}\) counter - clockwise rotation.

Step2: Check each option

• A \(90^{\circ}\) counter - clockwise rotation (\(90^{\circ}\text{ CCW}\)): standard rotation.
• A \(270^{\circ}\) clockwise rotation (\(270^{\circ}\text{ CW}\)): \(360^{\circ}- 90^{\circ}\text{ CCW}\), same as \(90^{\circ}\text{ CCW}\).
• A \(90^{\circ}\) leftward rotation: same as \(90^{\circ}\text{ CCW}\).
• A \(270^{\circ}\) counter - clockwise rotation (\(270^{\circ}\text{ CCW}\)): different from \(90^{\circ}\text{ CCW}\).

Answer:

a \(270^{\circ}\) counterclockwise rotation about the origin