Let b be the symmetry point of the river B 1 (that is, let BB 1⊥OX make BB 1= 1400).
Suppose the hydropower station is built at point C.
Materials for power transmission to two villages: d= AC+BC.
Connect AB 1 and BA 1 to point C.
Make OX⊥AA 1 at point c, and AE = a1e.
AC=A 1C in the same way BF = b1f.
d= AC+BC=A 1C+BC=A 1B
When A 1, b and c are in a straight line, d is the smallest.
The hydropower station is built at the intersection of the diagonal lines of the isosceles trapezoid. The most economical material.
Do ad⊥bb 1[ab = 500, BD=BF-DF=BF-AE=700-300=400] at point D.
AD=300。
b 1D = DF+b 1F = BF-BD+b 1D = 700-400+700 = 300+700 = 1000
ab 1 = a 1B = √( 90000+ 100000)= 100√ 109
RtACE△∽Rt△AB 1D
AE/B 1D=EC/AD
EC=90
The existing hydropower station is built at the vertical point from Village A to Xiaohe, 90 meters along the positive direction of X axis.