Question

question 3 of 12
select the correct answer.
using the distance formula, what is the approximate length of the line segment?
6.8 units
3.1 units
9.5 units
46.3 units

Explanation:

Step1: Identify endpoints

The endpoints of the segment are $(-4, -2)$ and $(3, 2)$.

Step2: Apply distance formula

The distance formula is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$. Substitute $x_1=-4, y_1=-2, x_2=3, y_2=2$:

$$ d=\sqrt{(3-(-4))^2+(2-(-2))^2} $$

Step3: Simplify the expression

Calculate differences first: $3-(-4)=7$, $2-(-2)=4$. Then square: $7^2=49$, $4^2=16$. Sum: $49+16=65$.

$$ d=\sqrt{65} $$

Step4: Approximate the value

$\sqrt{65}\approx8.06$, which is closest to 6.8 units (note: likely a typo in options, but 6.8 is the closest provided).

Answer:

6.8 units