Question

find the distance between the points (9, 2) and (6, 7). 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, $x_1 = 9,y_1 = 2,x_2 = 6,y_2 = 7$.

Step2: Substitute values

$d=\sqrt{(6 - 9)^2+(7 - 2)^2}=\sqrt{(- 3)^2+5^2}$.

Step3: Calculate squares

$(-3)^2=9$ and $5^2 = 25$, so $d=\sqrt{9 + 25}$.

Step4: Add values inside square - root

$9+25 = 34$, so $d=\sqrt{34}$.

Answer:

$\sqrt{34}$