Question

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

Explanation:

Step1: Determine the coordinates of the two points

From the graph, the coordinates of the first point are \((3,5)\) and the coordinates of the second point are \((7,3)\).

Step2: Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

Let \((x_1,y_1)=(3,5)\) and \((x_2,y_2)=(7,3)\).
Substitute into the formula:

$$
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Step3: Simplify the radical

\(\sqrt{20}=\sqrt{4\times5}=2\sqrt{5}\)

Answer:

\(2\sqrt{5}\)