
Find the distance between the points (1, 3) and (6, 13).

To find the distance between the points \((1, 3)\) and \((6, 13)\), we can use the distance formula, which is derived from the Pythagorean theorem:

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

Here, \((x_1, y_1) = (1, 3)\) and \((x_2, y_2) = (6, 13)\).

Substituting the values:

\[
d = \sqrt{(6 - 1)^2 + (13 - 3)^2}
\]
\[
d = \sqrt{5^2 + 10^2}
\]
\[
d = \sqrt{25 + 100}
\]
\[
d = \sqrt{125}
\]
\[
d = 5\sqrt{5}
\]

So, the distance between the points \((1, 3)\) and \((6, 13)\) is \(5\sqrt{5}\) units.

Would you like more details or explanations on this?

Here are 5 related questions:
1. How do you derive the distance formula?
2. What are some real-world applications of the distance formula?
3. How would the formula change if the points were in 3D space?
4. How does the distance formula relate to the Pythagorean theorem?
5. Can the distance between two points ever be negative?

**Tip**: Always check your calculations when subtracting coordinates to avoid errors in applying the formula.

Find the distance between the points (1, 3) and (6, 13).

Learn how to calculate the distance between the points (1, 3) and (6, 13) using the distance formula. This problem demonstrates key concepts in coordinate geometry and applies the Pythagorean theorem. Suitable for students in Grades 7-10.

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