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Crank
3 years ago
7

On a map, the distance between two towns is 3.4 inches. The map scale is 2 inches: 25 miles. What is the actual distance between

these towns?
Mathematics
1 answer:
Mariulka [41]3 years ago
4 0
For this question we can solve it by setting up a proportion:

\frac{2inches}{25 miles}= \frac{3.4inches}{x}

Now we can solve for x to find the total distance between the towns. Let's cross multiply and solve for x:

2x=85
x=42.5miles

So now we know that the total distance between the towns is 42.5 miles.
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use the eqn below to find the mid-pts

x-mid-pt = (x₁+x₂)/2

y-mid-pt = (y₁+y₂)/2

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So

midpoint JK = (-1+1/2, 1+3/2) = (0,2)

midpoint KL = (1+5/2, 3+⁻1/2) = (3,1)

midpoint LM = (5+⁻3/2, ⁻1+⁻1/2) = (1,-1)

midpoint MJ = (⁻3+⁻1/2, -1+1/2) = (-2,0)


use the eqn to find distance:


d = √(x₂ - x₁)² + (y₂ - y₁)²


Distance between JK and LM = √(0⁻1)² + (2 - ⁻1)² = √1 + 9 = √10

Distance between JM and KL = √(3-⁻2)² + (1-0)² = √25 + 1 = √26

Scale is 10

Actual distance = 10*(√10 + √26) = 82.6 = 83 units


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4 years ago
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