To solve the problem, we need to find the distance between points $A$ and $B$ on the grid using the distance formula:

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

Step-by-step solution:

1. Identify coordinates:

   • Point $A$ is at $(2, 1)$.
   • Point $B$ is at $(7, 6)$.

2. Plug values into the distance formula: $d = \sqrt{(7 - 2)^2 + (6 - 1)^2}$ $d = \sqrt{(5)^2 + (5)^2} = \sqrt{25 + 25} = \sqrt{50}$

3. Simplify: $d = \sqrt{50} \approx 7.07$

Final answer:

The distance between points $A$ and $B$ is approximately 7.07 units, rounded to the nearest hundredth.

Would you like further details or have any questions about the process?

Here are 5 related questions:

1. How is the distance formula derived from the Pythagorean theorem?
2. What happens if one of the points lies on the origin in this distance formula?
3. How do you find the midpoint of the line segment between two points?
4. How would the distance change if the grid units were different?
5. Can the distance formula be applied in three-dimensional space?

Tip: Always double-check your coordinate points before calculating the distance to avoid errors.