Question

find the distance between the points (-10, -5) and (-6, 0). 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 $(x_1,y_1)=(-10,-5)$ and $(x_2,y_2)=(-6,0)$. Then $x_2 - x_1=-6-(-10)=-6 + 10 = 4$ and $y_2 - y_1=0-(-5)=0 + 5 = 5$.

Step3: Calculate distance

Substitute into the formula: $d=\sqrt{4^2 + 5^2}=\sqrt{16 + 25}=\sqrt{41}$.

Answer:

$\sqrt{41}$