Question

△abc is the image of △abc under a rotation about the origin (0,0). determine the angles of rotation. choose all that apply. 90° clockwise 90° counter - clockwise 180° 270° clockwise 270° counter - clockwise

Explanation:

Step1: Analyze rotation rules

We know the rules of rotation about the origin for a point \((x,y)\). A \(90^{\circ}\) clock - wise rotation transforms \((x,y)\) to \((y, - x)\), a \(90^{\circ}\) counter - clockwise rotation transforms \((x,y)\) to \((-y,x)\), a \(180^{\circ}\) rotation transforms \((x,y)\) to \((-x,-y)\), a \(270^{\circ}\) clock - wise rotation is equivalent to a \(90^{\circ}\) counter - clockwise rotation and a \(270^{\circ}\) counter - clockwise rotation is equivalent to a \(90^{\circ}\) clock - wise rotation. By observing the positions of \(\triangle ABC\) and \(\triangle A'B'C'\) on the coordinate grid, we can see that the transformation from \(\triangle ABC\) to \(\triangle A'B'C'\) is a \(90^{\circ}\) clock - wise rotation.

Answer:

90° clockwise