Question

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

Explanation:

Step1: Identify the coordinates

From the graph, let's assume the two points are \((x_1, y_1) = (3, -9)\) and \((x_2, y_2) = (5, -4)\) (by observing the grid and the positions of the yellow dots).

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 \(x_1 = 3\), \(y_1 = -9\), \(x_2 = 5\), \(y_2 = -4\) into the formula:

First, calculate \(x_2 - x_1 = 5 - 3 = 2\) and \(y_2 - y_1 = -4 - (-9) = -4 + 9 = 5\).

Then, \(d = \sqrt{(2)^2 + (5)^2} = \sqrt{4 + 25} = \sqrt{29}\).

Answer:

\(\sqrt{29}\)