Question

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

Explanation:

Step1: Identify the coordinates

First, we identify the coordinates of the two points. From the graph, one point is \((-5, 0)\) and the other is \((-1, 4)\).

Step2: Apply the distance formula

The distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).
Substituting \(x_1 = -5\), \(y_1 = 0\), \(x_2 = -1\), and \(y_2 = 4\) into the formula:
\[

$$\begin{align*} d&=\sqrt{(-1 - (-5))^2 + (4 - 0)^2}\\ &=\sqrt{(-1 + 5)^2 + 4^2}\\ &=\sqrt{(4)^2 + 16}\\ &=\sqrt{16 + 16}\\ &=\sqrt{32}\\ &=\sqrt{16\times2}\\ &= 4\sqrt{2} \end{align*}$$

\]

Answer:

\(4\sqrt{2}\)