Question

find the distance between the points (2, 6) and (10, 0). 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 $(x_1,y_1)=(2,6)$ and $(x_2,y_2)=(10,0)$. Then $d=\sqrt{(10 - 2)^2+(0 - 6)^2}$.

Step3: Calculate the values inside the square - root

First, $(10 - 2)^2=8^2 = 64$ and $(0 - 6)^2=(-6)^2 = 36$. So $d=\sqrt{64 + 36}$.

Step4: Simplify the expression inside the square - root

$64+36 = 100$, so $d=\sqrt{100}$.

Step5: Find the square - root

$\sqrt{100}=10$.

Answer:

$10$