Find the exact length between points A & B, where A 
(4,1) and B (7,3).


To find the exact length between points \( A(4,1) \) and \( B(7,3) \), we use the distance formula:

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

Where:
- \( A(x_1, y_1) = (4, 1) \)
- \( B(x_2, y_2) = (7, 3) \)

Substituting the values:

\[
d = \sqrt{(7 - 4)^2 + (3 - 1)^2}
\]
\[
d = \sqrt{(3)^2 + (2)^2}
\]
\[
d = \sqrt{9 + 4} = \sqrt{13}
\]

So, the exact distance between points A and B is:

\[
\boxed{\sqrt{13}}
\]

Would you like more details or have any questions?

Here are 5 related questions to expand your knowledge:

1. How do you find the midpoint between two points?
2. What is the distance between two points in three-dimensional space?
3. How does the distance formula relate to the Pythagorean Theorem?
4. Can you find the distance between points on a coordinate plane with different units of measure?
5. How would you apply the distance formula in real-world scenarios?

**Tip:** Always remember that the distance formula is derived from the Pythagorean Theorem. It's essentially finding the hypotenuse of a right triangle formed by the points!

Find the exact length between points A & B, where A (4,1) and B (7,3).

Learn how to find the exact distance between points A(4,1) and B(7,3) using the distance formula. This guide provides a step-by-step solution, involving the Pythagorean Theorem and key geometry concepts. Suitable for Grades 8-10 students.

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