Question

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

Explanation:

Step1: Identify the coordinates

From the graph, the first point is \((6, 5)\) and the second point is \((8, 1)\).

Step2: Apply the distance formula

The distance formula between two points \((x_1, y_1)\) and \((x_2, y_2)\) is \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\).
Substitute \(x_1 = 6\), \(y_1 = 5\), \(x_2 = 8\), \(y_2 = 1\) into the formula:
\[

$$\begin{align*} d&=\sqrt{(8 - 6)^2 + (1 - 5)^2}\\ &=\sqrt{(2)^2 + (-4)^2}\\ &=\sqrt{4 + 16}\\ &=\sqrt{20}\\ &=\sqrt{4\times5}\\ &= 2\sqrt{5} \end{align*}$$

\]

Answer:

\(2\sqrt{5}\)