Question

find the distance between the points (10, 0) and (2, 6). 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 $(x_1,y_1)=(10,0)$ and $(x_2,y_2)=(2,6)$. Then $x_2 - x_1=2 - 10=-8$ and $y_2 - y_1=6 - 0 = 6$.

Step3: Calculate the squares

$(x_2 - x_1)^2=(-8)^2 = 64$ and $(y_2 - y_1)^2=6^2 = 36$.

Step4: Sum the squares

$(x_2 - x_1)^2+(y_2 - y_1)^2=64 + 36=100$.

Step5: Take the square - root

$d=\sqrt{100}=10$.

Answer:

10