https://file.aiquickdraw.com/mathbot/file/1726628751760495axxqf.jpg

To calculate the distance between cities A and B on the coordinate plane, we will use the distance formula:

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

From the graph:
- City A is located at point \( (-6, 0) \).
- City B is located at point \( (-3, 5) \).

Let's calculate the distance using these coordinates.

\[
d = \sqrt{((-3) - (-6))^2 + (5 - 0)^2}
\]

Now, I'll compute the distance.The distance between cities A and B is approximately 5.8 units.

Would you like further details or have any questions?

Here are some related questions for you to explore:
1. How would the distance change if city A moved to \((-4, 0)\)?
2. Can you calculate the midpoint between cities A and B?
3. What is the distance between city A and the origin \((0, 0)\)?
4. How can you apply the distance formula in three-dimensional space?
5. What happens if city B's coordinates become \((2, -1)\)? How does it affect the distance?

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

Use the map shown below to find the distance between cities A and B to the nearest tenth.

Find the distance between cities A and B on a coordinate plane using the distance formula. This step-by-step guide involves applying the formula √((x2 - x1)² + (y2 - y1)²) to calculate the distance. Suitable for students in Grades 7-9.

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