Use the map shown below to find the distance between cities A(0,0) and B (-4,6) to the nearest tenth.

To find the distance between two cities \( A(0,0) \) and \( B(-4,6) \), we can use the **distance formula**:

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

Given the coordinates:
- \( A(0, 0) \)
- \( B(-4, 6) \)

Let's plug these values into the formula:

\[
d = \sqrt{(-4 - 0)^2 + (6 - 0)^2}
\]

\[
d = \sqrt{(-4)^2 + (6)^2}
\]

\[
d = \sqrt{16 + 36}
\]

\[
d = \sqrt{52} \approx 7.2
\]

So, the distance between cities \( A \) and \( B \) is approximately **7.2 units**.

Would you like more details or have any questions?

Here are 5 related questions:
1. How do you derive the distance formula from the Pythagorean theorem?
2. What is the distance between points \( A(1, 1) \) and \( B(-3, 4) \)?
3. How do you find the midpoint between two points?
4. What is the significance of negative coordinates when calculating distances?
5. How do you calculate distances in three-dimensional space?

**Tip:** Always double-check the signs of coordinates when applying the distance formula to avoid errors.

Find the distance between cities A(0,0) and B(-4,6) using the distance formula. This step-by-step guide explains how to apply the Pythagorean Theorem in coordinate geometry. Perfect for students in Grades 7-9.

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