Question

find the distance between the points. (-12, 6), (3, -2)

Explanation:

Step1: Identify the 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, $x_1=-12,y_1 = 6,x_2 = 3,y_2=-2$.

Step2: Calculate the differences

First, find $x_2 - x_1$ and $y_2 - y_1$.
$x_2 - x_1=3-(-12)=3 + 12=15$.
$y_2 - y_1=-2 - 6=-8$.

Step3: Square the differences and sum them

$(x_2 - x_1)^2=15^2 = 225$ and $(y_2 - y_1)^2=(-8)^2 = 64$.
The sum is $(x_2 - x_1)^2+(y_2 - y_1)^2=225 + 64=289$.

Step4: Take the square - root

$d=\sqrt{289}=17$.

Answer:

$17$