Your itinerary contains a grid map of New York, with each unit on the grid representing 0.1250.125 miles. If the Rockefeller Center is located at (4,−2)(4,−2) and Central Park is located at (−11,6)(−11,6), what is the direct distance (not walking distance, which would have to account for bridges and roadways) between the two landmarks in miles? Round your answer to two decimal places, if necessary.

To find the direct distance between Rockefeller Center and Central Park on the grid map, we can use the **distance formula**:

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

Given the coordinates of Rockefeller Center at \((4, -2)\) and Central Park at \((-11, 6)\), we can substitute these values into the formula:

\[
d = \sqrt{((-11 - 4)^2 + (6 - (-2))^2)}
\]
\[
d = \sqrt{((-15)^2 + (8)^2)}
\]
\[
d = \sqrt{(225 + 64)}
\]
\[
d = \sqrt{289}
\]
\[
d = 17 \text{ units}
\]

Since each unit on the grid represents \(0.125\) miles, the actual distance is:

\[
\text{Distance} = 17 \times 0.125 = 2.125 \text{ miles}
\]

Thus, the direct distance between Rockefeller Center and Central Park is **2.13 miles** (rounded to two decimal places).

Would you like more details or have any questions about this?

Here are 5 related questions:
1. How would the walking distance be calculated if bridges or obstacles are involved?
2. What would the distance be if the grid units represented kilometers instead of miles?
3. How can you apply the distance formula to three-dimensional coordinates?
4. How would this problem change if one of the coordinates was shifted north by 2 units?
5. What is the relationship between the Pythagorean Theorem and the distance formula?

**Tip:** The distance formula is derived from the Pythagorean theorem, making it useful for calculating straight-line distances in coordinate systems.

Your itinerary contains a grid map of New York, with each unit on the grid representing 0.125 miles. If the Rockefeller Center is located at (4,−2) and Central Park is located at (−11,6), what is the direct distance (not walking distance, which would have to account for bridges and roadways) between the two landmarks in miles? Round your answer to two decimal places, if necessary.

Learn how to calculate the direct distance between Rockefeller Center and Central Park using the distance formula in coordinate geometry. The problem covers concepts like the Pythagorean theorem and how to convert grid units to miles. Suitable for Grades 9-10 students.

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