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To find the distance between points \( A \) and \( B \) on a coordinate grid, we can use the distance formula:

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

Looking at the grid, let's identify the coordinates of points \( A \) and \( B \):
1. \( A \) is at \( (1, 1) \)
2. \( B \) is at \( (5, 5) \)

Substituting these values into the formula:
\[
d = \sqrt{(5 - 1)^2 + (5 - 1)^2}
\]
\[
d = \sqrt{4^2 + 4^2}
\]
\[
d = \sqrt{16 + 16}
\]
\[
d = \sqrt{32}
\]
\[
d \approx 5.66
\]

So, the distance between \( A \) and \( B \) is approximately **5.66 units**.

Would you like a detailed breakdown of each calculation step?

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Here are some related questions:
1. How would the distance formula change in 3D coordinates?
2. How can you calculate the midpoint between two points?
3. What is the significance of the Pythagorean theorem in finding distances?
4. How would you find the slope between two points on a graph?
5. How can you verify calculations when using the distance formula?

**Tip:** Always double-check your coordinate points to avoid errors when applying the distance formula.

Find the distance between the points A and B given below. (That is, find the length of the segment connecting A and B.) Round your answer to the nearest hundredth.

Calculate the distance between points A and B on a coordinate grid using the distance formula. This guide provides a step-by-step solution and covers concepts in coordinate geometry and the Pythagorean theorem, suitable for students in Grades 8-10.

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