2. 
Amar drew the coordinates of the endpoints of QR¯¯¯¯¯¯¯¯
 at Q (8,2)
 and R (5,7)
.
 


Which measurement is closest to the length of QR¯¯¯¯¯¯¯¯
 in units Amar drew on the coordinate plane?

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!

Amar drew the coordinates of the endpoints of QR¯¯¯¯¯¯¯¯ at Q (8,2) and R (5,7). Which measurement is closest to the length of QR¯¯¯¯¯¯¯¯ in units Amar drew on the coordinate plane?

Learn how to calculate the distance between two points on a coordinate plane using the distance formula. This problem features points Q(8,2) and R(5,7), applying the Pythagorean theorem for an approximate result of 5.83 units. Suitable for students in Grades 6-8.

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