Question

find the distance between the points (-7, -6) and (-9, -4). 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, $x_1=-7$, $y_1 = - 6$, $x_2=-9$, $y_2=-4$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=-9-(-7)=-9 + 7=-2$, $y_2 - y_1=-4-(-6)=-4 + 6 = 2$.

Step3: Square the differences and sum

$(x_2 - x_1)^2=(-2)^2 = 4$, $(y_2 - y_1)^2=2^2 = 4$. Then $(x_2 - x_1)^2+(y_2 - y_1)^2=4 + 4=8$.

Step4: Calculate the distance

$d=\sqrt{8}=\sqrt{4\times2}=2\sqrt{2}$

Answer:

$2\sqrt{2}$