Question

find the distance between the two points in simplest radical form.

Explanation:

Step1: Identify the coordinates

Let the two points be $(x_1,y_1)$ and $(x_2,y_2)$. From the graph, assume the first - point is $(6,5)$ and the second point is $(9,1)$.

Step2: Apply the distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1 = 6,y_1 = 5,x_2 = 9,y_2 = 1$. Then $d=\sqrt{(9 - 6)^2+(1 - 5)^2}$.

Step3: Calculate the values inside the square - root

First, calculate $(9 - 6)^2=3^2 = 9$ and $(1 - 5)^2=(-4)^2 = 16$. Then $d=\sqrt{9 + 16}$.

Step4: Simplify the square - root

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

Answer:

$5$