what is the length of the segment?\n\nenter your answer, rounded to the nearest tenth, in the box.

Explanation:

Step1: Identify coordinates of endpoints

The endpoints of the segment are $X(-2, -2)$ and $Y(5, 3)$.

Step2: Apply the distance formula

$$d = \sqrt{(x_{2} - x_{1})^{2} + (y_{2} - y_{1})^{2}}$$

Step3: Substitute the coordinate values

$$d = \sqrt{(5 - (-2))^{2} + (3 - (-2))^{2}}$$

Step4: Simplify the expression

$$d = \sqrt{7^{2} + 5^{2}} = \sqrt{49 + 25} = \sqrt{74}$$

Step5: Calculate the numerical value

$$d \approx 8.6023$$

Step6: Round to the nearest tenth

$$d \approx 8.6$$

Answer:

8.6