To find the length of segment $PQ$, we use the distance formula:

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

Given the coordinates:

• $P = (2, 13)$
• $Q = (7, 1)$

Plug these into the distance formula:

$d = \sqrt{(7 - 2)^2 + (1 - 13)^2}$ $d = \sqrt{5^2 + (-12)^2}$ $d = \sqrt{25 + 144}$ $d = \sqrt{169}$ $d = 13$

The length of segment $PQ$ is 13 units.

Would you like more details or have any questions?

Here are five related questions to deepen your understanding:

1. How do you find the midpoint of segment $PQ$?
2. What is the length of segment $PR$?
3. How can the slope of segment $PQ$ be calculated?
4. What is the perimeter of triangle $PQR$?
5. How can you verify if triangle $PQR$ is a right triangle?

Tip: Always remember to double-check your subtraction of coordinates in distance calculations to avoid sign errors.