What Is the Axis of Symmetry?

Make the geometry a straight line that is axisymmetric or rotationally symmetric. After one part of the symmetrical figure rotates a certain angle around it, it coincides with the other part. Many figures have axes of symmetry. For example, an ellipse and a hyperbola have two axes of symmetry, and a parabola has one. The axis of symmetry of a regular cone or cylinder is a straight line that passes through the center of the bottom surface and the center of the vertex or the center of the other bottom surface. ^[1]

First introduce the concept of point symmetry about a line: if points A and B are in a straight line

On both sides, and

It's line AB

the distance between any point on the axis of symmetry and the point of symmetry, etc .;

The line segment connected by the symmetry point is bisected vertically by the axis of symmetry.

Corollary: If two figures are axisymmetric about a straight line, then the two figures are

Several common axisymmetric and centrally symmetric graphics: ^[2]

Axisymmetric graphics : line segments, corners, isosceles triangles, isosceles triangles, diamonds, rectangles, squares, isosceles trapezoids, circles, hyperbola (with two axes of symmetry), ellipse (with two axes of symmetry), parabola (with An axis of symmetry) and so on.

Number of symmetry axes : a corner has a symmetry axis, which is the angle bisector of the corner; an isosceles triangle has a symmetry axis, which is the vertical bisector of the bottom edge; an equilateral triangle has three symmetry axes, which are on three sides Vertical bisectors; the rhombus has two axes of symmetry, which are the straight lines where the two diagonal lines lie, and the rectangle has two axes of symmetry, which are the lines of the midpoint of the two opposite sides;

Center-symmetric graphics : line segments, parallelograms, rhombuses, rectangles, squares, circles, etc.

Center of symmetry: The center of symmetry of the line segment is the midpoint of the line segment; the center of symmetry of the parallelogram, rhombus, rectangle, and square is the intersection of the diagonals; the center of symmetry of the circle is the center of the circle.

Note: Line segments, diamonds, rectangles, squares, and circles are both axisymmetric and centrally symmetric graphics.

Axisymmetric transformation and center-symmetric transformation in the coordinate system:

The coordinate of the point P (x, y) with respect to the x-axis symmetric point P 1 is (x, -y), and the coordinate of the point P 2 with respect to the y-axis symmetry is (-x, y). Regarding the coordinates of the point P3 which is symmetrical about the origin, the rule of (-x, -y) can also be written as follows: the points on the y-axis (x-axis) symmetrical point have the same ordinate (abscissa) and abscissa (ordinate) Opposite each other. For the point where the origin is center-symmetric, the abscissa is the opposite number of the original abscissa, and the ordinate is the opposite number of the original ordinate, that is, the abscissa and ordinate are multiplied by -1. ^[2]