Question

find the distance between the points (3, 2) and (-9, -1). write your answer as a whole number or a fully simplified radical expression. do not round.

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, $x_1 = 3,y_1=2,x_2=-9,y_2 = - 1$.

Step2: Calculate differences

First, find $x_2 - x_1$ and $y_2 - y_1$. $x_2 - x_1=-9 - 3=-12$ and $y_2 - y_1=-1 - 2=-3$.

Step3: Square the differences

$(x_2 - x_1)^2=(-12)^2 = 144$ and $(y_2 - y_1)^2=(-3)^2 = 9$.

Step4: Sum the squared - differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=144 + 9=153$.

Step5: Take the square - root

$d=\sqrt{153}=\sqrt{9\times17}=3\sqrt{17}$

Answer:

$3\sqrt{17}$