Origin Center Symmetry, What is Origin Symmetry?

Central symmetry and central symmetry are two different but closely related concepts The difference between them is: central symmetry refers to the mutual positional relationship between two congruent figures, these two figures are symmetrical about one point, this point is the center of symmetry, and the symmetry of two figures about points is also called central symmetry In two figures with central symmetry, all the symmetry points of all points on one of them are on the other graph, and conversely, the symmetry points of all points on the other graph are all on this graph; And the central symmetry figure refers to a figure itself is centered symmetrical All the points on the center of symmetry on the center of symmetry are on the figure itself If the two figures with a center symmetry are regarded as a whole (one figure), then this figure is a central symmetry figure; A centrally symmetrical figure, if the symmetrical part is seen as two figures, then they are again about the central symmetry

That is to say: Centrally symmetrical graph: If a graph is rotated 180 degrees around a certain point and can coincide with itself, then we say that the graph forms a centrally symmetrical graph.

Central symmetry: If a graph is rotated 180 degrees around a point and can coincide with another figure, then we say that the two graphs form a central symmetry.

There are both axisymmetric and centrally symmetrical figures: straight lines, line segments, two intersecting lines, rectangles, diamonds, squares, circles, etc

There are only center-symmetrical figures: parallelograms, etc

Figures that are neither axisymmetric nor centrally symmetrical are: unequal triangles, non-isosceles trapezoids, etc

Origin center symmetry is the meaning of origin as the center and center symmetry.

An image with the origin as the center of symmetry.

The origin center symmetry figure is only a center graph about the origin, that is, a figure can coincide with itself after rotating 180 degrees around the origin, while the origin center symmetry refers to the symmetry of two figures about the origin center, that is, a figure can coincide with another figure after rotating 180 degrees around the origin.

An image that is rotated 180 degrees in the x0y plane according to the origin and can coincide with the original image.

It turns out that the horizontal and vertical semi-axes of the graph are the opposite of the two numbers.

Origin symmetry refers to the symmetry of a graph, function, or object with respect to the origin of a coordinate system. When a graph, function, or object is symmetrical at the origin of the coordinate system, each of its points has a point of symmetry, such that the line segments that connect the two points pass through the origin, and the line segments are of equal length.

Specifically, for a graph on a plane, if any of the points are mirrored with respect to the origin, the point is still on the graph, then the graph is symmetrical at the origin.

For a function, if the value of the function is the same as the value of the function when x is a positive number, i.e., there is f(-x) = f(x), then the function is symmetrical at the origin.

For an object, if the points obtained by mirroring each of its points with respect to the origin are still on the object, then the object is origin symmetrical.

Origin symmetry is a special type of symmetry that differs from other symmetries such as x-axis symmetry, y-axis symmetry. Origin symmetry has important applications and significance in the fields of geometry, algebra, and object and auction theory.

Origin symmetry is a geometric phenomenon in mathematics where the origin is the intersection of the x-axis and y-axis. Any point of the odd function has a point of symmetry, and the point of symmetry of a point (x,y) on the Cartesian coordinate system with respect to the origin is (-x,-y).

If any x in the definition domain and any y in the domain of a function f(x) have f(- x) =f(x), and the definition domain is also symmetrical about the origin, then f(x) is said to be an odd function (that is, if any point (x,y) of the function f(x) has a symmetry point, it is called an odd function).

Origin symmetry means that in the Cartesian coordinate system, the distance between a point symmetrical point with respect to the origin point is equal to that point, and the angle between the two points and the x-axis is 180 degrees. For a function, if the definition domain of the function is symmetric with respect to the origin, and there is f(-x)=-f(x) for any x in the definition domain and any y in the value range, then the function is an odd function.

To understand origin symmetry in mathematics, we must first understand that the intersection of the x-axis and y-axis in the Cartesian coordinate system (i.e., the x,y coordinate axis) is called the origin.

When there is a point (x,y) on the coordinate axis (where x,y is a positive value), and its symmetry point is (- x, - y) in the same coordinate system, these two points are called origin symmetrical ascension, the point (x,y) just pointed to is the point of the first quadrant (the upper right of the Cartesian coordinate system), and (x,-y) is the point of the third quadrant (the bottom left of the Cartesian coordinate system).

Odd functions. If any x in the definition domain and any y in the domain of a function f(x) have f(- x) =f(x), and the definition domain is also symmetrical about the origin, then f(x) is said to be an odd function (that is, if any point (x,y) of the function f(x) has a symmetry point, it is called an odd function).

Symmetry with respect to origin means that in a Cartesian coordinate system, the symmetry point of a point (x,y) is (-x,-y) in the same coordinate system. This means that the distance of these points is equal. Any point of the odd function has a symmetry point, i.e., any x in the definition domain of the function and any y in the value range have f(-x) = f(x).

Draw two number axes that are perpendicular to each other and have a common origin in the plane, where the horizontal axis is the x-axis and the vertical axis is the y-axis, so that we say that the plane Cartesian coordinate system is established on the plane, referred to as the Cartesian coordinate system. It is also divided into the first quadrant, the second quadrant, the third quadrant, and the fourth quadrant.