Question

find the distance between the points (-5, -3) and (-10, -4). 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 $(x_1,y_1)=(-5,-3)$ and $(x_2,y_2)=(-10,-4)$. Then $x_2 - x_1=-10-(-5)=-10 + 5=-5$ and $y_2 - y_1=-4-(-3)=-4 + 3=-1$.

Step3: Substitute into the formula

$d=\sqrt{(-5)^2+(-1)^2}=\sqrt{25 + 1}=\sqrt{26}$.

Answer:

$\sqrt{26}$