Question

△abc is the image of △abc under a rotation about the origin, (0, 0). determine the angles of rotation. choose all answers that apply: a 90° clockwise b 90° counterclockwise c 180° d 270° clockwise e 270° counterclockwise

Explanation:

Step1: Recall rotation rules

A 90 - degree clockwise rotation of a point $(x,y)$ about the origin gives $(y, - x)$. A 90 - degree counter - clockwise rotation of a point $(x,y)$ about the origin gives $(-y,x)$. A 180 - degree rotation of a point $(x,y)$ about the origin gives $(-x,-y)$. A 270 - degree clockwise rotation of a point $(x,y)$ about the origin gives $(-y,x)$ and a 270 - degree counter - clockwise rotation of a point $(x,y)$ about the origin gives $(y, - x)$.

Step2: Analyze the transformation

Let's take a general point in $\triangle ABC$ and its corresponding point in $\triangle A'B'C'$. If we consider the orientation of the triangle, we can see that the transformation from $\triangle ABC$ to $\triangle A'B'C'$ is a 90 - degree counter - clockwise rotation or a 270 - degree clockwise rotation. For example, if we assume a point $(x,y)$ in $\triangle ABC$, its image in $\triangle A'B'C'$ follows the rule of 90 - degree counter - clockwise rotation $(-y,x)$.

Answer:

B. 90° counterclockwise
D. 270° clockwise