Question

find the distance between the points (8, 3) and (5, 7). 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 $(x_1,y_1)=(8,3)$ and $(x_2,y_2)=(5,7)$. Then $d=\sqrt{(5 - 8)^2+(7 - 3)^2}$.

Step3: Calculate the values inside the square - root

First, $(5 - 8)^2=(-3)^2 = 9$ and $(7 - 3)^2=4^2 = 16$. So $d=\sqrt{9 + 16}$.

Step4: Simplify the square - root

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

Answer:

5