Question

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．

Answer 1

1) A在x轴的负半轴上,n < 0

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