Question

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

Explanation:

Step1: Recall rotation rules

When a point $(x,y)$ is rotated 90 - degrees counter - clockwise around the origin, it becomes $(-y,x)$; 180 - degrees counter - clockwise, it becomes $(-x,-y)$; 270 - degrees counter - clockwise, it becomes $(y, - x)$; 360 - degrees counter - clockwise, it remains $(x,y)$.

Step2: Analyze the transformation of $\triangle ABC$

By observing the coordinates of the vertices of $\triangle ABC$ and $\triangle A'B'C'$, we can see that the sign of both the $x$ and $y$ coordinates of each vertex of $\triangle ABC$ has changed to get the vertices of $\triangle A'B'C'$. This is the rule for a 180 - degree counter - clockwise rotation around the origin.

Answer:

180 degrees