Question

12 multiple choice 1 point △abc has been rotated ______ counter - clockwise around the origin. 180 degrees 90 degrees 360 degrees 270 degrees

Explanation:

Step1: Recall rotation rules

For a 90 - degree counter - clockwise rotation around the origin, the transformation rule for a point $(x,y)$ is $(-y,x)$. For a 180 - degree counter - clockwise rotation, the rule is $(-x,-y)$. For a 270 - degree counter - clockwise rotation, the rule is $(y, - x)$. For a 360 - degree rotation, the point returns to its original position.

Step2: Analyze the transformation of points

Let's assume a point $(x,y)$ in $\triangle ABC$. If we observe the transformation of the triangle to $\triangle A'B'C'$, we can see that the transformation rule applied is $(-y,x)$. For example, if we consider a vertex of $\triangle ABC$ and its corresponding vertex in $\triangle A'B'C'$, we find that the coordinates follow the 90 - degree counter - clockwise rotation rule.

Answer:

90 degrees