Question

find the distance between the points (-7, -1) and (-5, -10). 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, $(x_1,y_1)=(-7,-1)$ and $(x_2,y_2)=(-5,-10)$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=-5-(-7)=-5 + 7 = 2$, and $y_2 - y_1=-10-(-1)=-10 + 1=-9$.

Step3: Square the differences

Square the results from step 2. $(x_2 - x_1)^2=2^2 = 4$ and $(y_2 - y_1)^2=(-9)^2 = 81$.

Step4: Sum the squared - differences

Add the squared differences: $(x_2 - x_1)^2+(y_2 - y_1)^2=4 + 81=85$.

Step5: Take the square - root

$d=\sqrt{85}$

Answer:

$\sqrt{85}$