Question

find the distance between the points (2, 2) and (9, 8). write your answer as a whole number or a fully simplified radical expression. do not round. units

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 $(x_1,y_1)=(2,2)$ and $(x_2,y_2)=(9,8)$. Then $x_2 - x_1=9 - 2 = 7$ and $y_2 - y_1=8 - 2 = 6$.

Step3: Calculate the distance

$d=\sqrt{7^2+6^2}=\sqrt{49 + 36}=\sqrt{85}$.

Answer:

$\sqrt{85}$