A (x0, y0) straight line Ax+By+C=0.

Let B(x 1, y 1) be the symmetrical point of a point about a straight line.

Then a (x0+x1)/2+b (y0+y1)/2+c = 0.

A(y 1-y0)=B(x 1-x0) can solve the equation.

It is worth noting that if y=x+c or y =-x+c is symmetric.

Then the equation can be directly substituted, for example, A(x0, y0) makes B(x 1, y 1) a point, and the symmetrical point about the line y=x+c = x0+c, x=y-c=y, 0-c, b (x0+c).

Second, the method steps of finding a point about the symmetrical point of a straight line:

1, set a symmetrical point about a straight line, then the midpoint of the two points is on this straight line;

2, and two straight lines are perpendicular to the known straight lines, the product of their slopes is negative one;

3. Solve according to the above equation about the abscissa and ordinate of the symmetrical point;

4. You can get the coordinates of the symmetry point.

Extended data:

Symmetrical point refers to the point on one side of a straight line and the corresponding point on the other side in a plane figure according to certain laws, so that these two points have a symmetrical relationship with the straight line. In other words, after the mirror is turned over, these two points and the figure surrounded by the straight line completely coincide. This symmetrical point is on a straight line to describe this symmetrical relationship.

Symmetry point plays an important role in geometry, because it can help us better understand the drawn plane figure, which is essential in many fields. In many cases, symmetrical design exists in buildings, such as gorgeous churches, castles, ancient architectural relics and so on. In addition, the symmetry point also has important mathematical significance, which is closely related to algebra, group theory and other mathematical branches.

In a word, symmetry point is an important concept in geometry, which can help us better describe and understand plane graphics and is one of the keys in various fields. In daily life, symmetrical design is also very common, because the aesthetic feeling of symmetry plays an important role in people's minds.