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Correct Answer: 2.15.
to calculate the average slope between two points on a topographical map, you must first understand two key pieces of information: the vertical distance (elevation change) and the horizontal distance between these points. the slope is essentially how steeply the land rises or falls, which can be quantified by the ratio of the rise in elevation to the horizontal distance (also known as the "run").
2.15.* in this example, the horizontal distance between points a and c is given as 2 inches on the map. if the map's scale is such that 1 inch represents 100 feet, then 2 inches represents 200 feet in real-world horizontal distance.
2.15.* next, we need to determine the vertical distance or elevation change between these two points. let's assume the elevation at point a (the lowest point) is 210 feet and at point c (the summit) is 640 feet. the elevation change (rise) between these points is then calculated by subtracting the elevation at point a from the elevation at point c:
\[ \text{elevation change} = 640 \, \text{feet} - 210 \, \text{feet} = 430 \, \text{feet} \]
2.15.* with both the rise and run known, the average slope can be calculated using the formula for slope \( m \), which is the rise divided by the run:
\[ m = \frac{\text{rise}}{\text{run}} = \frac{430 \, \text{feet}}{200 \, \text{feet}} = 2.15 \]
this value, 2.15, represents the average feet of elevation gained per foot of horizontal distance between points a and c.
2.15.* this slope ratio indicates that for every foot you travel horizontally from a to c, you ascend approximately 2.15 feet in elevation. this is a relatively steep slope, indicating that the terrain rises sharply between these two points.
by understanding how to read and interpret both horizontal and vertical distances on a topographical map, and applying the formula for slope, one can effectively determine the steepness of any segment of terrain between two points, regardless of whether a direct, straight-line path is feasible.
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