Students are designing a new town as part of a social studies project on urban planning. ey want to place the town’s high school
at point A and the middle school at point B. they also plan to build roads that run directly from point A to the mall and from point B to the mall. the average cost to build a road in this area is $550,000 per mile. . c. Draw the road from point A to the mall and find its length. d. Draw the road from point B to the mall and find its length. e. How much farther from the mall is point B than point A? How much more will it cost to build the longer road?
1 answer:
Answer:
c, d. see attached
e. about 2.96 miles; about $1.63 million
Step-by-step explanation:
e. The x-coordinates of points A and B are 1/3 and 2/3 of the x-coordinate of "Downtown", respectively. The y-coordinates of A and B are 2/3 and 1/3 of the y-coordinate of "Town pool", respectively. Then the distances from A and B to the Mall can be found using the Pythagorean theorem:
A to Mall = √(4² +(10/3)²) = √(244/9) ≈ 5.20683 . . . miles
B to Mall = √(8² +(5/3)²) = √(601/9) ≈ 8.17177 . . . miles
The difference in distance is ...
(BM -AM) = 8.17177 -5.20683 = 2.96493 . . . miles
The mall is about 2.96 miles farther from point B than from point A.
The additional cost is the difference in miles multiplied by the cost per mile:
(2.96 mi)($0.550 M/mi) = $1.63 M
The additional cost of the longer road is about $1.63 million.
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