A. Two villages B are on the same side of the straight river CD. The distances from villages a and B to the river are AC = 1km, BD = 3km and CD = 3km respectively. Now we need to build a water plant on the riverside CD to deliver tap water to villages a and B. the cost of laying the pipeline is 20000 yuan per kilometer. Please choose the location of the water plant on the CD and make a point O, so as to save the cost of laying the pipeline and find out the cost of laying the pipeline Total cost

A. Two villages B are on the same side of the straight river CD. The distances from villages a and B to the river are AC = 1km, BD = 3km and CD = 3km respectively. Now we need to build a water plant on the riverside CD to deliver tap water to villages a and B. the cost of laying the pipeline is 20000 yuan per kilometer. Please choose the location of the water plant on the CD and make a point O, so as to save the cost of laying the pipeline and find out the cost of laying the pipeline Total cost

According to the meaning of the topic, as long as we find a point o on the straight line L to minimize the sum of the distances from point O to a and B. make a symmetrical point a 'of point a about the straight line L and connect a' B, then the sum of the distances from the intersection point O of a 'B and the straight line L to a and B is minimum, and OA + ob = OA' + ob = a 'B. cross point a' and make a vertical line to BD, intersect the extension line of BD at point E, at RT △ a 'be According to Pythagorean theorem, a ′ B = 5 (km), that is, the minimum length of laying water pipe is 5 km. Therefore, the minimum cost of laying water pipe is 5 × 2 = 100000 yuan

How to find the shortest distance by Pythagorean theorem

Two points are direct and the line segment is shortest

As shown in the figure, villages a and B are on the same side of the riverbank CD. The distance between villages a and B and the riverbank is AC = 1km, BD = 3km and CD = 3km respectively. Now a water plant is to be built on the riverbank CD to deliver tap water to villages a and B. the engineering cost of laying water pipes is 20000 yuan per kilometer. Please select the location o of the water plant on the CD to save the cost of laying water pipes and calculate the total cost of laying water pipes

As shown in the figure, point O is the location of the water plant, ∵ AC = 1km, BD = 3km, CD = 3km, ∵ AE = AC + CE = AC + DB ′ = AC + BD = 1 + 3 = 4km, B ′ e = CD = 3km, ab ′ = AE2 + B ′ E2 = 42 + 32 = 5km, the length of laying water pipe is: Ao + ob = Ao + ob ′ = ab ′ = 5km, the engineering cost of laying water pipe is 20 per kilometer

As shown in the figure, it is known that villages a and B are on the same side of the river CD, and their distances to the river are AC = 10 km, BD = 30 km, and CD = 30 km respectively. Now we need to build a water plant P on the river to supply water to villages a and B. It is known that the cost of laying water pipes is 20000 yuan per kilometer. Please choose the location P of water plant on the river CD, so as to save the cost of laying water pipes The total cost at this time can be calculated

According to the meaning of the topic, as long as we find a point P on the straight line L to minimize the sum of distances from point P to a and B. make a symmetrical point a 'of point a about the straight line L and connect a' B, then the sum of distances from the intersection point P of a 'B and the straight line L to a and B is the minimum, and PA + Pb = PA' + Pb = a 'B; According to Pythagorean theorem, a ′ e = CD = 30, be = BD + de = 40, a ′ B = 50 (km), that is, the minimum length of laying water pipe is 50 km. Therefore, the minimum cost of laying water pipe is 50 × 2 = 1 million yuan