Question

question 4 · 1 point
find the distance between the points (-8, -5) and (2, -3).
give an exact answer in simplest radical form. do not round.
provide your answer below:

Explanation:

Step1: Identify distance - formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.
Here, $x_1=-8,y_1 = - 5,x_2=2,y_2=-3$.

Step2: Substitute values

Substitute the values into the formula:
\[

$$\begin{align*} d&=\sqrt{(2-(-8))^2+((-3)-(-5))^2}\\ &=\sqrt{(2 + 8)^2+(-3 + 5)^2}\\ &=\sqrt{(10)^2+(2)^2}\\ &=\sqrt{100 + 4}\\ &=\sqrt{104} \end{align*}$$

\]

Step3: Simplify the radical

Factor 104: $104=4\times26$. Then $\sqrt{104}=\sqrt{4\times26}=2\sqrt{26}$.

Answer:

$2\sqrt{26}$