Question

find the distance between the points (0, -3) and (3, -5). write your answer as a whole number or a fully simplified radical expression. do not round.

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 $(x_1,y_1)=(0, - 3)$ and $(x_2,y_2)=(3,-5)$. Then $x_2 - x_1=3 - 0 = 3$ and $y_2 - y_1=-5-(-3)=-5 + 3=-2$.

Step3: Substitute into formula

$d=\sqrt{(3)^2+(-2)^2}=\sqrt{9 + 4}=\sqrt{13}$.

Answer:

$\sqrt{13}$