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Answer:
The shortest distance is 2.2 miles
Step-by-step explanation:
we know that
The shortest distance you must travel to reach the river is the perpendicular distance to the river
step 1
Find the slope of the line perpendicular to the river
we have
The slope of the river is m=3
Remember that if two lines are perpendicular, then their slopes are opposite reciprocal (the product of their slopes is -1)
therefore
The slope of the line perpendicular to the river is
step 2
Find the equation of the line into point slope form
we have
substitute
step 3
Find the intersection point of the river and the line perpendicular to the river
we have
------> equation A
-----> equation B
Solve the system by graphing
The intersection point is (-0.1,1,7)
see the attached figure
step 3
Find the distance between the points (2,1) and (-0,1,1.7)
the formula to calculate the distance between two points is equal to
substitute
