Question

find the distance between (6,6) and (10,9). show your work! leave your answer under the radical unless it is a perfect square.

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: Assign values

Let $(x_1,y_1)=(6,6)$ and $(x_2,y_2)=(10,9)$. Then $x_2 - x_1=10 - 6 = 4$ and $y_2 - y_1=9 - 6 = 3$.

Step3: Substitute into formula

$d=\sqrt{(4)^2+(3)^2}=\sqrt{16 + 9}=\sqrt{25}$.

Step4: Simplify

$\sqrt{25}=5$.

Answer:

$5$