## symmetry over origin

### Symmetry over the origin refers to a specific type of symmetry in mathematics

Symmetry over the origin refers to a specific type of symmetry in mathematics. It occurs when a figure or object remains exactly the same when rotated by 180 degrees around the origin (the point (0, 0) on a coordinate plane) or reflected across the origin.

To understand symmetry over the origin, let’s consider a point (x, y) in a coordinate system. When a figure exhibits this type of symmetry, the image of the point will be (-x, -y) after the transformation.

For example, let’s take a simple figure such as a line segment connecting two points A and B. If point A has coordinates (-2, 3), then the reflection or rotation over the origin would place point A at (2, -3) since its x-coordinate changes sign and its y-coordinate changes sign as well. Similarly, point B would be reflected to (-4, 1) if it has coordinates (4, -1) originally.

If a figure exhibits symmetry over the origin, then any other point on that figure will also have a corresponding point after the transformation that is an equal distance from the origin but in the opposite direction.

Symmetry over the origin can be visualized in various mathematical objects, such as straight lines passing through the origin, circles centered at the origin, and certain polygons centered at the origin. In general, any figure that is symmetric over the origin will have equal distances between corresponding points on opposite sides of the origin.

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