Question

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

Explanation:

Step1: Identify the coordinates of the two points.

From the graph, the first point (let's call it \( A \)) is at \( (-8, 0) \) and the second point (let's call it \( B \)) is at \( (-6, 3) \).

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 \( x_1 = -8 \), \( y_1 = 0 \), \( x_2 = -6 \), and \( y_2 = 3 \) into the formula:
\[

$$\begin{align*} d &= \sqrt{(-6 - (-8))^2 + (3 - 0)^2}\\ &= \sqrt{(-6 + 8)^2 + 3^2}\\ &= \sqrt{(2)^2 + 9}\\ &= \sqrt{4 + 9}\\ &= \sqrt{13} \end{align*}$$

\]

Answer:

\(\sqrt{13}\)