Which of the following is the shortest distance from the starting point A to the rest stop E? A. 33.54 miles B. 65.12 miles C. 15 miles D. 80.78 miles

Steps to Solve

1. Identify the coordinates of points A and E

From the diagram, locate the coordinates of point A and point E.

• Point A is at ( (0, 50) )
• Point E is at ( (30, -20) )

2. Calculate the distance using the distance formula

The distance between two points ( (x_1, y_1) ) and ( (x_2, y_2) ) can be calculated using the formula:

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

Plugging in the coordinates of points A and E:

$$ d = \sqrt{(30 - 0)^2 + (-20 - 50)^2} $$

3. Perform the calculations

Calculate ( (30 - 0)^2 ) and ( (-20 - 50)^2 ):

• ( (30 - 0)^2 = 30^2 = 900 )
• ( (-20 - 50)^2 = (-70)^2 = 4900 )

Now substitute these values back into the distance formula:

$$ d = \sqrt{900 + 4900} = \sqrt{5800} $$

4. Simplify the distance

Now calculate ( \sqrt{5800} ):

• ( \sqrt{5800} = 76.16 )

5. Convert the distance to miles

Since each grid represents 5 miles, convert the distance:

$$ \text{Distance in miles} = \frac{d}{5} = \frac{76.16}{5} \approx 15.23 \text{ miles} $$

However, this distance must be rounded and checked against the given options.