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!