When y=4, x=4∴B is (4,4).

(2) ① When x=0, y=- 1/4x? +8=8∴A is (0,8),

20cm = 0.002m，

When y=8-0.002, x = 2 √ (8-y) = 0.04 √ 500m ≈ 894cm,

When y=8-0.002×2, x = 2 √ (8-y) = 0.04 √ 100 m ≈ 1265 cm, 1265-894=37 1 cm.

When y=8-0.002×3, x = 2 √ (8-y) = 0.04 √ 1549- 1265=284 cm.

The length of the first three steps is about 894 cm, 37 1 cm and 284 cm respectively.

(2) the length of each step is not less than 20cm.

∴ length of step n = 0.04 √ (5n)-0.04 √ [5 (n-1)] ≥ 0.002 √ n-√ (n-1) ≥ 0.01√ 5.

∴∴n≤50 1 This kind of step can't be paved all the way to the foot of the mountain.

(when y=8-0.002×50 1, x=2√(8-y)≈2.002 hundred meters = 20020cm；; When y=8-0.002×502, x=2√(8-y)≈2.003996 m =20039.96 cm, 20039.96-20020= 19.96 cm < 20 cm).

(3) Set the hanging height of the ropeway station to W.

W= 1/28(x- 16)？ - 1/4(x-8)？ ∴ The maximum value W =8/3, and the maximum suspension height of ropeway station is 8/300m.