Question

find the distance between the points (-5, -4) and (0, -9). write your answer as a whole number or a fully simplified radical expression. do not round. units

Explanation:

Step1: Identify distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Assign values

Let $(x_1,y_1)=(-5,-4)$ and $(x_2,y_2)=(0,-9)$. Then $x_2 - x_1=0-(-5)=5$ and $y_2 - y_1=-9 - (-4)=-5$.

Step3: Substitute into formula

$d=\sqrt{(5)^2+(-5)^2}=\sqrt{25 + 25}=\sqrt{50}$.

Step4: Simplify radical

$\sqrt{50}=\sqrt{25\times2}=5\sqrt{2}$.

Answer:

$5\sqrt{2}$