Question

what is true about the rotation of the shaded triangle to the position of the unshaded triangle? choose two correct answers.
the rotation is 90° counterclockwise about the origin.
the rotation uses the rule (x,y)→(-y,x).
the rotation is 90° clockwise about the origin.
the rotation uses the rule (x,y)→(-x,-y).

Explanation:

Step1: Recall rotation rules

For a \(90^{\circ}\) clockwise rotation about the origin, the rule is \((x,y)\to(y, - x)\). For a \(90^{\circ}\) counter - clockwise rotation about the origin, the rule is \((x,y)\to(-y,x)\).

Step2: Analyze the direction of rotation

Looking at the position of the shaded and unshaded triangles, the rotation is \(90^{\circ}\) counter - clockwise about the origin.

Step3: Check the rotation rule

Since it is a \(90^{\circ}\) counter - clockwise rotation about the origin, the rule \((x,y)\to(-y,x)\) is used.

Answer:

The rotation is \(90^{\circ}\) counterclockwise about the origin; The rotation uses the rule \((x,y)\to(-y,x)\)