Question

find the distance between the two points (-3, -2) and (-12, -14). the distance is
(type an exact answer, using radicals as needed)

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, $x_1=-3,y_1 = - 2,x_2=-12,y_2=-14$.

Step2: Calculate differences

$x_2 - x_1=-12-(-3)=-12 + 3=-9$ and $y_2 - y_1=-14-(-2)=-14 + 2=-12$.

Step3: Square the differences

$(x_2 - x_1)^2=(-9)^2 = 81$ and $(y_2 - y_1)^2=(-12)^2=144$.

Step4: Sum the squared - differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=81 + 144=225$.

Step5: Take the square - root

$d=\sqrt{225}=15$.

Answer:

$15$