To find the center of rotation, we need to identify corresponding points on the original and rotated figures. Here we have triangle ABC and its rotated version A'B'C'. We'll use points A and B with their corresponding points A' and B' to locate the center of rotation.
The first step is to connect corresponding points with line segments. We draw a line from A to A' and another line from B to B'. These segments represent the paths that each point traveled during the rotation. The center of rotation lies somewhere along the perpendicular bisectors of these connecting segments.
Now we construct the perpendicular bisectors. First, we find the midpoint of segment AA' and draw a line perpendicular to it through this midpoint. Then we do the same for segment BB'. These perpendicular bisectors are crucial because the center of rotation is equidistant from corresponding points, so it must lie on both perpendicular bisectors.
The intersection of the two perpendicular bisectors gives us the center of rotation. This special point is equidistant from each pair of corresponding points. We can verify this by drawing a circle centered at this point - it passes through both A and A', confirming that our center is correct. The same circle would also pass through B and B'.
To summarize, finding the center of rotation involves four key steps: identify corresponding points, connect them with line segments, construct perpendicular bisectors, and find their intersection. This method is universal and works for any rotation. Watch as we demonstrate this with a continuous rotation - the center remains fixed while the figure rotates around it.