Question

find the distance between the points (-4, -4) and (-2, -10). write your answer as a whole number or a fully simplified radical expression. do not round.

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, $x_1=-4,y_1 = - 4,x_2=-2,y_2=-10$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=-2-(-4)=2$, $y_2 - y_1=-10 - (-4)=-6$.

Step3: Square the differences

$(x_2 - x_1)^2=2^2 = 4$, $(y_2 - y_1)^2=(-6)^2 = 36$.

Step4: Sum the squared - differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=4 + 36=40$.

Step5: Take the square - root

$d=\sqrt{40}=\sqrt{4\times10}=2\sqrt{10}$.

Answer:

$2\sqrt{10}$