Set the coordinates (a, b) of the search point. According to the set point (a, b) and the known point (c, d), the coordinates of the symmetrical point (a+c/2, b+d/2) can be expressed, and the symmetrical point is on a straight line, so if this point is substituted into a straight line, the coordinates of the sought point can be obtained.

The general formula of the straight line is y=kx+b, where k is the slope, so the slope of the straight line y=-x+ 1 is-1, and the straight line connected by two symmetrical points about the straight line is perpendicular to the symmetrical straight line. Because the product of the slopes of two vertical lines is-1, the slope of AB is-1-1=1.

Extended data:

The symmetry problem of a point about a straight line is a generalization of the symmetry problem of a point about a point. There are two main aspects to deal with this kind of problem: the product of the slope of the connecting line between two points and the known straight line is equal to-1, and the midpoint of the two points is on the known straight line.

The symmetry problem of a straight line about a point can be transformed into the symmetry problem of a point on a straight line. It should be noted that two symmetrical straight lines are parallel, and we often use parallel straight line system to solve them.

Solve it by using a symmetrical straight line that must be parallel to the known straight line, and then the distance between the point (symmetry center) and the two straight lines is equal. The second solution is to transform it into a point-to-point symmetry problem, get the coordinates of the symmetrical point by using the midpoint coordinate formula, and then write the linear equation by using the linear equations.

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