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The problem asks to find the distance \( d \) between two points \( A(1, 0) \) and \( B(5, 2) \) using the distance formula:

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

Where:
- \( A(x_1, y_1) = (1, 0) \)
- \( B(x_2, y_2) = (5, 2) \)

Substituting these coordinates into the formula:

\[
d = \sqrt{(5 - 1)^2 + (2 - 0)^2}
\]

\[
d = \sqrt{(4)^2 + (2)^2}
\]

\[
d = \sqrt{16 + 4}
\]

\[
d = \sqrt{20}
\]

\[
d \approx 4.47
\]

Rounded to the nearest tenth, the distance \( d \) is approximately \( 4.5 \).

Would you like more details or have any further questions?

Here are 5 related questions for further understanding:
1. What is the significance of using the distance formula in coordinate geometry?
2. How does the distance formula relate to the Pythagorean theorem?
3. Can the distance between points be negative, and why or why not?
4. How would the formula change if we were working in three dimensions?
5. What are the coordinates of the midpoint between points A and B?

**Tip:** Always verify that the coordinates are accurately substituted into the distance formula to avoid mistakes.

Find the distance, d, of AB. A = (1, 0) B = (5, 2)

Learn how to find the distance between two points on a coordinate plane using the distance formula. This guide provides a step-by-step calculation for the distance between points A (1,0) and B (5,2), perfect for students in grades 6-8 exploring coordinate geometry.

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