1. First, determine the coordinates of known points and straight lines. Let the known point be A(x 1, y 1) and the equation of the straight line be y = kx+b, and find the slope k and intercept b of the straight line. The slope k can be calculated by knowing the point A and any point B(x2, y2) on the straight line, that is, k=(y2-y 1)/(x2-x 1).

2. Intercept b can be calculated by substituting the known point A into the linear equation y=kx+b, that is, b=y 1-k*x 1. Find the distance d from a known point a to a straight line. The distance d can be calculated by the following formula: d = | k * x1-y1+b |/sqrt (k 2+1). Find the coordinates of the known point a about the symmetrical point c of the line.

3. The coordinates of the symmetry point C can be calculated by the following formula: C(x3, y3)=(x 1+d *( 1/k), y 1+d *( 1/k)). Finally, verify whether the symmetry point C is on a straight line. If the symmetry point C is on a straight line, then it is the symmetry point of the known point A about the straight line; Otherwise, it is necessary to reselect the known point A or straight line, or check whether there are any errors in the calculation process.

The Concept of Symmetry Point and Related Knowledge

1, symmetry point is a common concept in geometry and algebra. In geometry, if a point P has a point P in a plane or space, so that the distance from the origin to P is equal to the distance of two straight lines to P, then we call P the symmetrical point of P. ..

2. In algebra, for any complex number Z on the complex plane, its real part and imaginary part are symmetrical about the origin, that is, if z=x+yi (where X and Y are real numbers and I are imaginary units), then the symmetry point of Z is -x+yi.

3. The knowledge of symmetry points can be applied to many different fields. For example, in geometry, we often use symmetry points to find the symmetry axis or center of a shape. In physics, symmetry is an important concept, which can be used to describe many natural phenomena, such as crystal structure, electromagnetic field and so on. In algebra, symmetry is also an important tool to study the properties of functions.

4. In addition, symmetry point is also an important concept in graphic design. For example, a circle, a square or a rectangle can obtain a new figure by rotating, flipping or translating its symmetry. The application of this symmetry in design can create beautiful and harmonious patterns and structures.