Question

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

Explanation:

Step1: Identify coordinates

First, find the coordinates of the two points. From the graph, let's assume the first point (left) is \((-2, 6)\) and the second point (right) is \((5, 3)\).

Step2: Apply 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 \(x_1 = -2\), \(y_1 = 6\), \(x_2 = 5\), \(y_2 = 3\):
\(d = \sqrt{(5 - (-2))^2 + (3 - 6)^2}\)
\(= \sqrt{(7)^2 + (-3)^2}\)
\(= \sqrt{49 + 9}\)
\(= \sqrt{58}\)

Answer:

\(\sqrt{58}\)