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 two points are \((-1,4)\) and \((7,-8)\).

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

Here, \(x_1=-1,y_1 = 4,x_2=7,y_2=-8\).
Substitute into the formula:

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Step3: Simplify \(\sqrt{208}\)

Factor \(208\): \(208=16\times13\).
So \(\sqrt{208}=\sqrt{16\times13}=\sqrt{16}\times\sqrt{13}=4\sqrt{13}\)

Answer:

\(4\sqrt{13}\)