Question

12 a figure is graphed on a coordinate grid and then rotated. if (x, y) is a point on the original figure, which ordered pair represents the corresponding point after the transformation? use the checkmarks to select the correct answer in each row.
transformation | (-y, x) | (-x, -y) | (y, -x)
a 90° counterclockwise rotation about the origin. | | |
a 180° counterclockwise rotation about the origin. | | |
a 90° clockwise rotation about the origin. | | |
a 180° clockwise rotation about the origin. | | |

Explanation:

Step1: Recall rotation rules

• \(90^\circ\) counterclockwise rotation about origin: \((x,y)\to(-y,x)\)
• \(180^\circ\) (counter)clockwise rotation about origin: \((x,y)\to(-x,-y)\) (since \(180^\circ\) rotation is same clockwise/counterclockwise)
• \(90^\circ\) clockwise rotation about origin: \((x,y)\to(y,-x)\)

Step2: Match each transformation

• \(90^\circ\) counterclockwise: Check \((-y,x)\)
• \(180^\circ\) counterclockwise: Check \((-x,-y)\)
• \(90^\circ\) clockwise: Check \((y,-x)\)
• \(180^\circ\) clockwise: Check \((-x,-y)\) (same as \(180^\circ\) counterclockwise)

Answer:

Transformation	\((-y,x)\)	\((-x,-y)\)	\((y,-x)\)
\(180^\circ\) counterclockwise rotation about the origin.	❌	✔️	❌
\(90^\circ\) clockwise rotation about the origin.	❌	❌	✔️
\(180^\circ\) clockwise rotation about the origin.	❌	✔️	❌