SOLUTION: A grand tour of four cities begins at city A and makes successive stops at cities B, C, and D before returning to city A. If the cities are located as shown in the accompanying fig

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Question 665825: A grand tour of four cities begins at city A and makes successive stops at cities B, C, and D before returning to city A. If the cities are located as shown in the accompanying figure, find the total distance covered on the tour. (Give your answer correct to the nearest mile.)
. miles
(Graph is not drawn to exact scale. Coordinates of cities are listed below the graph for reference.)

City A (0, 0), City B (450, 300), City C (-810, 760), City D (-810, 0)

Answer by MathLover1(20850) About Me  (Show Source):
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City A (0, 0), City B (450, 300), City C (-810, 760), City D (-810, 0)
first find the distance between cities
City A (0, 0), City B (450, 300)
Solved by pluggable solver: Distance between two points in two dimensions
The distance (denoted by d) between two points in two dimensions is given by the following formula:

d=sqrt%28%28x1-x2%29%5E2+%2B+%28y1-y2%29%5E2%29

Thus in our case, the required distance is
d=sqrt%28%280-450%29%5E2+%2B+%280-300%29%5E2%29=+540.832691319598+


For more on this concept, refer to Distance formula.



City B (450, 300), City C (-810, 760)

Solved by pluggable solver: Distance between two points in two dimensions
The distance (denoted by d) between two points in two dimensions is given by the following formula:

d=sqrt%28%28x1-x2%29%5E2+%2B+%28y1-y2%29%5E2%29

Thus in our case, the required distance is
d=sqrt%28%28450--810%29%5E2+%2B+%28300-760%29%5E2%29=+1341.34261096858+


For more on this concept, refer to Distance formula.



City C (-810, 760), City D (-810, 0)
Solved by pluggable solver: Distance between two points in two dimensions
The distance (denoted by d) between two points in two dimensions is given by the following formula:

d=sqrt%28%28x1-x2%29%5E2+%2B+%28y1-y2%29%5E2%29

Thus in our case, the required distance is
d=sqrt%28%28-810--810%29%5E2+%2B+%28760-0%29%5E2%29=+760+


For more on this concept, refer to Distance formula.



City D (-810, 0),City A (0, 0)
Solved by pluggable solver: Distance between two points in two dimensions
The distance (denoted by d) between two points in two dimensions is given by the following formula:

d=sqrt%28%28x1-x2%29%5E2+%2B+%28y1-y2%29%5E2%29

Thus in our case, the required distance is
d=sqrt%28%28-810-0%29%5E2+%2B+%28760-0%29%5E2%29=+1110.72048689128+


For more on this concept, refer to Distance formula.


the total distance covered on the tour will be equal to sum all distances above:
AB%2BBC%2BCD%2BDA=540.83%2B1341.34%2B760%2B1110=3752.17miles