To solve the problems, we need more information about the specific coordinates of Las Plumas and Bently on the coordinate system. However, I can guide you on how you might approach each part of the problem using hypothetical coordinates.
A. Finding the total length of the highway:
Let's say the coordinates for Las Plumas are \( (x_1, y_1) \) and for Bently are \( (x_2, y_2) \).
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Calculate the distance between the two points using the distance formula: \[ \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
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Convert the distance from units on the coordinate system to kilometers: Since each unit represents 10 kilometers, you will multiply the calculated distance by 10 to get the total length in kilometers.
B. Finding the coordinates of the rest area:
To find the rest area located \( \frac{3}{5} \) of the way from Las Plumas to Bently, you can follow these steps:
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Find the directional vector from Las Plumas to Bently: \[ \text{Direction Vector} = (x_2 - x_1, y_2 - y_1) \]
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Calculate the point \( \frac{3}{5} \) of the way: The coordinates of the rest area can be found by taking \( \frac{3}{5} \) of the way along the directional vector from Las Plumas: \[ \text{Coordinates of Rest Area} = \left( x_1 + \frac{3}{5}(x_2 - x_1), y_1 + \frac{3}{5}(y_2 - y_1) \right) \]
This means that for each coordinate (x and y), you will calculate a position that is three-fifths of the distance from Las Plumas to Bently.
Summary
- For Part A, use the distance formula and convert units to find the total highway length.
- For Part B, compute the coordinates that represent three-fifths of the way from Las Plumas to Bently using vector arithmetic.
If you have the specific coordinates, you can substitute them into these formulas to get the numerical answers!
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