平面直角坐标系中,已知点P坐标为(m,n) 那么点P关于直线y=kx+b（k≠0）的对称点p′的坐标为?

直线y=kx+b斜率为k, 其垂线斜率为-1/k
过P的垂线方程为: y - n = (-1/k)(x - m)
与y = kx + b联立得交点为Q((kn - kb + m)/(k² + 1), (k²n +km + b)/(k² + 1))
Q为PP'的中点, P'(p, q)
(m + p)/2 = (kn - kb + m)/(k² + 1), p = 2(kn - kb + m)/(k² + 1) - m = (2kn - 2kb + m - k²m)/(k² + 1)
(n + q)/2 = (k²n +km + b)/(k² + 1), q = 2(k²n +km + b)/(k² + 1) - n = (k²n +2km + 2b - n)/(k² + 1)
P'((2kn - 2kb + m - k²m)/(k² + 1), (k²n +2km + 2b - n)/(k² + 1))