Rotating a shape 180 degrees around the origin makes each point travel double its original distance from the origin.
When a shape is rotated 180 degrees around the origin, each point on the shape will travel a total distance of twice its original distance from the origin.
Here's why:
1. Rotation by 180 degrees reverses the direction of each point. Imagine each point as a vector extending from the origin. Rotating by 180 degrees flips this vector directly back on itself.
2. The reversed vector travels the same distance as the original one.** Since the reversed vector essentially retraces the path of the original vector, the total distance traveled is double the original distance**.
Therefore, regardless of the shape or its initial position, rotating it 180 degrees around the origin will make each point travel a distance equal to twice its original distance from the origin.