Question

find the distance between the points (-5, -5) and (0, -8). 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 $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Let $(x_1,y_1)=(-5,-5)$ and $(x_2,y_2)=(0,-8)$.

Step2: Substitute values

$d=\sqrt{(0 - (-5))^2+((-8)-(-5))^2}=\sqrt{(0 + 5)^2+(-8 + 5)^2}=\sqrt{5^2+(-3)^2}$.

Step3: Calculate squares

$\sqrt{5^2+(-3)^2}=\sqrt{25 + 9}$.

Step4: Simplify

$\sqrt{25+9}=\sqrt{34}$.

Answer:

$\sqrt{34}$