Question

which coordinate represents the images center of rotation?

Explanation:

Step1: Recall rotation property

The center of rotation is the point that stays fixed during a rotation. We can find it by observing the intersection of the perpendicular - bisectors of the line segments connecting corresponding points of the pre - image and the image.

Step2: Identify corresponding points

Let's take two corresponding points. For example, a point on the pre - image and its rotated counterpart.

Step3: Construct perpendicular - bisectors

Construct the perpendicular - bisectors of the line segments connecting corresponding points. The intersection of these perpendicular - bisectors is the center of rotation. In this case, by visual inspection or by using the property that for a rotation, if we consider the transformation of the pre - image to the image, we can see that the center of rotation is the origin $(0,0)$.

Answer:

$(0,0)$