Question

find the distance between the points (-3, -4) and (-2, -9). 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 $(x_1,y_1)=(-3,-4)$ and $(x_2,y_2)=(-2,-9)$. Then $x_2 - x_1=-2-(-3)=-2 + 3=1$ and $y_2 - y_1=-9-(-4)=-9 + 4=-5$.

Step3: Substitute into formula

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

Answer:

$\sqrt{26}$