Question

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

Explanation:

Step1: Identify distance - formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Substitute the given points

Let $(x_1,y_1)=(6,6)$ and $(x_2,y_2)=(2,9)$. Then $x_2 - x_1=2 - 6=-4$ and $y_2 - y_1=9 - 6 = 3$.

Step3: Calculate the squares and sum

$(x_2 - x_1)^2=(-4)^2 = 16$ and $(y_2 - y_1)^2=3^2 = 9$. The sum is $16 + 9=25$.

Step4: Find the square - root

$d=\sqrt{25}=5$.

Answer:

5