Question

find the distance between the points (-4, 3) and (-5, -5). 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, $x_1=-4,y_1 = 3,x_2=-5,y_2=-5$.

Step2: Substitute values

$d=\sqrt{(-5-(-4))^2+(-5 - 3)^2}=\sqrt{(-5 + 4)^2+(-8)^2}$.

Step3: Calculate the squares

$d=\sqrt{(-1)^2+64}=\sqrt{1 + 64}$.

Step4: Simplify the expression

$d=\sqrt{65}$

Answer:

$\sqrt{65}$