Question

find the distance between the points (-7, -7) and (3, -2). 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, $x_1=-7,y_1 = - 7,x_2=3,y_2=-2$.

Step2: Calculate $(x_2 - x_1)^2$

$x_2 - x_1=3-(-7)=3 + 7=10$, so $(x_2 - x_1)^2=10^2 = 100$.

Step3: Calculate $(y_2 - y_1)^2$

$y_2 - y_1=-2-(-7)=-2 + 7 = 5$, so $(y_2 - y_1)^2=5^2=25$.

Step4: Calculate the distance

$d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}=\sqrt{100 + 25}=\sqrt{125}=\sqrt{25\times5}=5\sqrt{5}$.

Answer:

$5\sqrt{5}$ units