Question

find the distance between the points (2, -2) and (-3, -1). write your answer as a whole number or a fully simplified radical expression. do not round. units

Explanation:

Step1: Recall 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, $x_1 = 2,y_1=-2,x_2=-3,y_2 = - 1$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=-3 - 2=-5$ and $y_2 - y_1=-1-(-2)=-1 + 2 = 1$.

Step3: Square the differences

Square the results from Step 2. $(-5)^2=25$ and $1^2 = 1$.

Step4: Sum and find square - root

Sum the squared values: $25 + 1=26$. Then, $d=\sqrt{26}$ units.

Answer:

$\sqrt{26}$ units