Question

question 3 of 5 select the correct answer. using the distance formula, what is the approximate length of the line segment? 9.5 units 3.1 units 46.3 units 6.8 units

Explanation:

Step1: Identify the endpoints

The endpoints of the line - segment are approximately $(- 3,-2)$ and $(2,2)$.

Step2: Recall the distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step3: Substitute the values

Here, $x_1=-3,y_1 = - 2,x_2 = 2,y_2 = 2$. Then $d=\sqrt{(2-(-3))^2+(2 - (-2))^2}=\sqrt{(2 + 3)^2+(2 + 2)^2}=\sqrt{5^2+4^2}=\sqrt{25 + 16}=\sqrt{41}$.

Step4: Calculate the approximate value

$\sqrt{41}\approx6.4$ (since $6^2=36$ and $7^2 = 49$, and $41$ is closer to $36$). The closest value among the options is $6.8$ units.

Answer:

6.8 units