Question

find the distance between the two points in simplest radical form. (-3,6) and (-8,-6)

Explanation:

Step1: Identify distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1=-3,y_1 = 6,x_2=-8,y_2=-6$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=-8-(-3)=-8 + 3=-5$. $y_2 - y_1=-6 - 6=-12$.

Step3: Square the differences

$(x_2 - x_1)^2=(-5)^2 = 25$ and $(y_2 - y_1)^2=(-12)^2=144$.

Step4: Sum the squared - differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=25 + 144=169$.

Step5: Take square - root

$d=\sqrt{169}=13$.

Answer:

$13$