There are two cases: 1, and the straight line l 1 is parallel to the straight line l3 (axis of symmetry), so that we can know the slope of the straight line (if it exists), establish the equation of the straight line l2 (oblique type), and calculate the value of b by using the distance formula between two parallel lines.
2. The straight line l 1 intersects with the straight line l3 (axis of symmetry). First find the intersection point, then establish the equation of the straight line l2 (point inclination), take any point on the straight line l3 (outside the intersection point), and use the distance from this point to l 1 and l2 to find the slope.
For example, given that the straight line L 1 and the straight line L2: 2x-y-2 = 0 are symmetrical about the straight line L3: x-2y- 1 = 0, find the equation L 1.
L2:2x-y-2=0。 ( 1)
L3:x-2y- 1=0。 (2)
x= 1，y=0
A( 1，0)
L 1:y=k*(x- 1)，kx-y-k=0
L3:x-2y- 1=0
x=3，y= 1
|3*2- 1-2|√5=|3k- 1-k|/√( 1+k^2)
k=-2/ 1 1
l 1:2x+ 1 1y-2 = 0