Question

find the distance between the points (9, -6) and (-2, -4). write your answer as a whole number or a fully simplified radical expression. do not round. units

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, $x_1 = 9,y_1=-6,x_2=-2,y_2 = - 4$.

Step2: Calculate the differences

First, find $x_2 - x_1$ and $y_2 - y_1$.
$x_2 - x_1=-2 - 9=-11$.
$y_2 - y_1=-4-(-6)=-4 + 6 = 2$.

Step3: Square the differences and sum them

$(x_2 - x_1)^2=(-11)^2 = 121$.
$(y_2 - y_1)^2=2^2 = 4$.
The sum is $121+4=125$.

Step4: Take the square - root

$d=\sqrt{125}=\sqrt{25\times5}=5\sqrt{5}$

Answer:

$5\sqrt{5}$ units