Question

find the distance between the points (5, 1) and (9, 4). 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

Here, $x_1 = 5,y_1 = 1,x_2 = 9,y_2 = 4$. So $d=\sqrt{(9 - 5)^2+(4 - 1)^2}$.

Step3: Calculate the values inside the square - root

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

Step4: Simplify the square - root

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

Answer:

5