https://file.aiquickdraw.com/mathbot/file/1726078450719mqnewaw0.jpg

To find the distance between points A and B on the graph, we can use the distance formula:

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

Let's determine the coordinates of points A and B from the graphs in the image:

1. **First graph**: 
   - Point A is at (1, 2)
   - Point B is at (8, 6)

   Applying the formula:

   \[
   \text{Distance} = \sqrt{(8 - 1)^2 + (6 - 2)^2} = \sqrt{7^2 + 4^2} = \sqrt{49 + 16} = \sqrt{65} \approx 8.1
   \]

2. **Second graph**:
   - Point A is at (1, 7)
   - Point B is at (8, 2)

   Applying the formula:

   \[
   \text{Distance} = \sqrt{(8 - 1)^2 + (2 - 7)^2} = \sqrt{7^2 + (-5)^2} = \sqrt{49 + 25} = \sqrt{74} \approx 8.6
   \]

So, the distances AB are approximately **8.1** and **8.6**, correct to one decimal place.

Would you like more details or have any questions?

### Additional Related Questions
1. How do you use the distance formula for 3D coordinates?
2. What are the alternative methods to find the distance between two points on a grid?
3. How do you find the midpoint between two points on a coordinate plane?
4. Can the distance formula be used for non-linear paths?
5. What are real-world applications of the distance formula?

### Tip:
Always double-check the coordinates you are using when applying the distance formula to avoid errors.

Find the distance AB. Give your answers correct to 1 decimal place.

Learn how to calculate the distance between two points A and B using the distance formula derived from Pythagoras' Theorem. The problem involves determining distances on a coordinate plane and is suitable for students in Grades 7-9.

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