Question

1. use the distance formula to find the distance from (-2,-1) to (-5,-6). round your answer to two decimal places.

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, $(x_1,y_1)=(-2,-1)$ and $(x_2,y_2)=(-5,-6)$.

Step2: Substitute values

Substitute $x_1=-2$, $y_1 = - 1$, $x_2=-5$, $y_2=-6$ into the formula:
\[

$$\begin{align*} d&=\sqrt{(-5-(-2))^2+(-6 - (-1))^2}\\ &=\sqrt{(-5 + 2)^2+(-6 + 1)^2}\\ &=\sqrt{(-3)^2+(-5)^2}\\ &=\sqrt{9 + 25}\\ &=\sqrt{34} \end{align*}$$

\]

Step3: Calculate and round

$\sqrt{34}\approx5.83$

Answer:

$5.83$