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.