According to the nature of axial symmetry, the midpoint of y = b and aa' is on the straight line x=k, then,

(a+x)/2=k，x=2k-a

So it is easy to find the coordinates of A' (2k-a, b).

2. When the straight line is perpendicular to the Y axis.

According to the nature of axial symmetry, the midpoint of x = a and bb' is on the straight line y=k, then,

(y+b)/2=k，y=2k-b

So it is easy to find the coordinate (a, 2k-b) of b'

3. When a straight line is a general straight line, its general form can be expressed as y=kx+b, and transformed into the form of straight line Ax+By+C=0.

(a, b) The coordinates of the symmetrical point about the straight line Ax+By+C=0 are

From the point of view of plane analytic geometry, a straight line on a plane is a graph represented by a binary linear equation in a plane rectangular coordinate system.

Related knowledge points:

1, two points A(x 1, y 1), and the coordinate of the middle point c of B(x2, y2) is [(x 1+ x2)/2, (y1+y2)/2];

2. If two points are symmetrical about a straight line, the midpoint of these two points is on this straight line (symmetry axis). If the straight line y=k 1x+b 1 and the straight line y=k2x+b2? Perpendicular to each other, then k 1k2=- 1.

3. Point-to-line symmetrical point drawing: make the intersection point perpendicular to the straight line and extend it into a', so that the distance from it to the straight line is equal.