Question

find the distance between the points (-5, -6) and (-4, -9). 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, $x_1=-5,y_1 = - 6,x_2=-4,y_2=-9$.

Step2: Calculate differences

$x_2 - x_1=-4-(-5)=-4 + 5=1$ and $y_2 - y_1=-9-(-6)=-9 + 6=-3$.

Step3: Substitute into formula

$d=\sqrt{(1)^2+(-3)^2}=\sqrt{1 + 9}=\sqrt{10}$.

Answer:

$\sqrt{10}$