Question

find the length of the segment. round to two decimal places if necessary.

Explanation:

Step1: Identify segment endpoints

The endpoints are $(-3, 1)$ and $(-6, -9)$.

Step2: Apply distance formula

The distance formula is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$.
Substitute $x_1=-3, y_1=1, x_2=-6, y_2=-9$:
$d=\sqrt{(-6-(-3))^2+(-9-1)^2}$

Step3: Simplify inside the square root

Calculate differences:
$d=\sqrt{(-3)^2+(-10)^2}=\sqrt{9+100}$

Step4: Compute final value

$d=\sqrt{109}\approx10.44$

Answer:

10.44