Suppose that a certain linear grid coordinate system has been overlaid on a map
ID: 470314 • Letter: S
Question
Suppose that a certain linear grid coordinate system has been overlaid on a map of the United States. The grid numbers are calibrated in miles, and there is a road circuitry factor of 1.21. Find the expected road distances between the following pairs of points:
Location
X-Coordinate
Y-Coordinate
From
Lansing, MI
924.3
1675.2
To
Lubbock, TX
1488.6
2579.4
From
El Paso, TX
1696.3
2769.3
To
Atlanta, GA
624.9
2318.7
From
Boston, MA
374.7
1326.6
To
Los Angeles, CA
2365.4
2763.9
From
Seattle, WA
2668.8
1900.8
Portland, OR
2674.2
2039.7
Location
X-Coordinate
Y-Coordinate
From
Lansing, MI
924.3
1675.2
To
Lubbock, TX
1488.6
2579.4
From
El Paso, TX
1696.3
2769.3
To
Atlanta, GA
624.9
2318.7
From
Boston, MA
374.7
1326.6
To
Los Angeles, CA
2365.4
2763.9
From
Seattle, WA
2668.8
1900.8
Portland, OR
2674.2
2039.7
Explanation / Answer
Solution is in two two steps
Step 1: Find the straight line distance between the two points. The formula to find the straight line distance is ((x2 - x1)^2 + (y2 - y1)^2)^0.5, where x1, y1 are the coordinates of origin and x2, y2 are the coordinates of destination.
Step 2: Multiply the straight line distance by the road circuitry factor to get the expected road distance.
Location X-Coordinate Y-Coordinate Straight Line Distance (miles) Expected Road Distance (miles) From Lansing, MI 924.3 1675.2 1065.8 1289.7 To Lubbock, TX 1488.6 2579.4 From El Paso, TX 1696.3 2769.3 1162.3 1406.4 To Atlanta, GA 624.9 2318.7 From Boston, MA 374.7 1326.6 2455.3 2971.0 To Los Angeles, CA 2365.4 2763.9 From Seattle, WA 2668.8 1900.8 139.0 168.2 Portland, OR 2674.2 2039.7Related Questions
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