Question

find the distance between the points (2, 1) and (5, 5). write your answer as a whole number or a fully simplified radical expression. do not round.

Explanation:

Step1: Identify the 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

Here, $x_1 = 2,y_1 = 1,x_2 = 5,y_2 = 5$. So $d=\sqrt{(5 - 2)^2+(5 - 1)^2}$.

Step3: Calculate the values inside the square - root

$(5 - 2)^2=3^2 = 9$ and $(5 - 1)^2=4^2 = 16$. Then $d=\sqrt{9 + 16}$.

Step4: Simplify the expression

$9+16 = 25$, so $d=\sqrt{25}=5$.

Answer:

5