To find the length of the line segment $QR$ on a coordinate plane, we use the distance formula:

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

Where:

• $Q(x_1, y_1) = (8, 2)$
• $R(x_2, y_2) = (5, 7)$

Substitute the values into the formula:

$d = \sqrt{(5 - 8)^2 + (7 - 2)^2}$ $d = \sqrt{(-3)^2 + (5)^2}$ $d = \sqrt{9 + 25}$ $d = \sqrt{34} \approx 5.83$

So, the length of $QR$ is approximately 5.83 units.

Would you like more details or have any questions?

Here are some related questions:

1. What is the distance formula used for in geometry?
2. How do you find the midpoint between two points on a coordinate plane?
3. How can we apply the Pythagorean theorem to this distance problem?
4. What are the coordinates of a point that divides the segment into a particular ratio?
5. How can you calculate the slope of the line through points Q and R?

Tip: Always double-check your calculations by redoing each step, especially when using square roots!