Question

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

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

Step2: Calculate differences

$x_2 - x_1=4 - 6=-2$ and $y_2 - y_1=2 - 6=-4$.

Step3: Square the differences

$(x_2 - x_1)^2=(-2)^2 = 4$ and $(y_2 - y_1)^2=(-4)^2 = 16$.

Step4: Sum the squared - differences

$(x_2 - x_1)^2+(y_2 - y_1)^2=4 + 16=20$.

Step5: Take the square - root

$d=\sqrt{20}=\sqrt{4\times5}=2\sqrt{5}$.

Answer:

$2\sqrt{5}$