Question

find the distance between the points (6, -9) and (-6, -10). 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 $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Let $(x_1,y_1)=(6,-9)$ and $(x_2,y_2)=(-6,-10)$.

Step2: Calculate $x_2 - x_1$ and $y_2 - y_1$

$x_2 - x_1=-6 - 6=-12$, $y_2 - y_1=-10-(-9)=-10 + 9=-1$.

Step3: Substitute into distance formula

$d=\sqrt{(-12)^2+(-1)^2}=\sqrt{144 + 1}=\sqrt{145}$.

Answer:

$\sqrt{145}$