如图,直角梯形OABC的腰OC在y轴的正半轴上,点A（5n,0）在x轴的负半轴上,OA :AB :OC=5 :5 :3．点D是线段OC上一点,且OD＝BD．（1）若直线y＝kx＋m（k≠0）过B、D两点,求k的值；（2）在（1）的条件下,反比例函数y＝ x (m) 的图象经过点B．①求证：反比例函数y＝ x (m) 的图象与直线AB必有两个不同的交点；②已知点P（p,－n－1）,Q（q,－n－2）在线段AB上,当点E落在线段PQ上时,求n的取值范围．

(1) A在x轴的负半轴上, n OA = -|5n, OA : OC = 5 : 3, OC = -3n
设B(b, -3n), B在x轴上的垂足为E(b, 0)
AB² = AE² + BE²
(-5n)² = (b - 5n)² + (-3n)²
b = 9n (在A左侧. 舍去)
或b = n
B(n, -3n)
设D(0, d), OD = d, BD = √[(n - 0)² + (-3n - d)²] = √[n² + (3n + d)²]
OD = BD, d = -5n/3
D(0, -5n/3)
k = BD的斜率 = (-3n + 5n/3)/(n - 0) = -4/3
(2)
m = D的纵坐标 = -5n/3
反比例函数 y = m/x = -5n/(3x)
取x = n, y = -5/3
题有问题

1) A在x轴的负半轴上,n OA = -|5n,OA :OC = 5 :3,OC = -3n
设B(b,-3n),B在x轴上的垂足为E(b,0)
AB² = AE² + BE²
(-5n)² = (b - 5n)² + (-3n)²
b = 9n (在A左侧.舍去)
或b = n
B(n,-3n)
设D(0,d),OD = d,BD = √[(n - 0)² + (-3n - d)²] = √[n² + (3n + d)²]
OD = BD,d = -5n/3
D(0,-5n/3)
k = BD的斜率 = (-3n + 5n/3)/(n - 0) = -4/3