Question

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

Explanation:

Step1: Identify the coordinates

Let the first - point be $(x_1,y_1)$ and the second - point be $(x_2,y_2)$. From the graph, assume the first point is $(5, - 9)$ and the second point is $(8,-6)$.

Step2: Apply the distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Substitute $x_1 = 5,y_1=-9,x_2 = 8,y_2=-6$ into the formula:
\[

$$\begin{align*} d&=\sqrt{(8 - 5)^2+(-6+9)^2}\\ &=\sqrt{3^2+3^2}\\ &=\sqrt{9 + 9}\\ &=\sqrt{18}\\ &=\sqrt{9\times2}\\ &=3\sqrt{2} \end{align*}$$

\]

Answer:

$3\sqrt{2}$