Question

find the distance between the two points in simplest radical form.
(6, -1) and (-2, -9)

Explanation:

Step1: Recall distance formula

The distance $d$ between $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

Step2: Assign coordinates

Let $(x_1,y_1)=(6,-1)$, $(x_2,y_2)=(-2,-9)$

Step3: Substitute values

$d=\sqrt{(-2-6)^2+(-9-(-1))^2}$

Step4: Calculate differences

$d=\sqrt{(-8)^2+(-8)^2}$

Step5: Compute squares

$d=\sqrt{64+64}$

Step6: Sum and simplify radical

$d=\sqrt{128}=\sqrt{64\times2}=8\sqrt{2}$

Answer:

$8\sqrt{2}$