Question

find the distance between the points (-5, -4) and (-1, 5). write your answer as a whole number or a fully simplified radical expression. do not round. units

Explanation:

Step1: Identify the 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 the values of the points

Let $(x_1,y_1)=(-5,-4)$ and $(x_2,y_2)=(-1,5)$. Then $x_2 - x_1=-1-(-5)=-1 + 5 = 4$ and $y_2 - y_1=5-(-4)=5 + 4 = 9$.

Step3: Substitute into the formula

$d=\sqrt{(4)^2+(9)^2}=\sqrt{16 + 81}=\sqrt{97}$.

Answer:

$\sqrt{97}$