Question

1. the coordinate grid shows triangle abc. triangle abc is rotated 270° counterclockwise about the origin to create triangle abc. which rule describes this transformation? a. (x,y)→(-x,-y) b. (x,y)→(y,x) c. (x,y)→(-y,x) d. (x,y)→(y,-x)

Explanation:

Step1: Recall rotation rules

The rule for a \(270^{\circ}\) counter - clockwise rotation about the origin is \((x,y)\to(y, - x)\).

Step2: Verify with an example

Let's take a point \((x,y)\). After a \(90^{\circ}\) counter - clockwise rotation \((x,y)\to(-y,x)\), after a \(180^{\circ}\) counter - clockwise rotation \((x,y)\to(-x,-y)\), after a \(270^{\circ}\) counter - clockwise rotation \((x,y)\to(y, - x)\)

Answer:

D. \((x,y)\to(y, - x)\)