Question

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

Explanation:

1. First, assume the two - point formula:

• The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
• From the graph, assume the first point is \((x_1,y_1)=(2,1)\) and the second point is \((x_2,y_2)=(3, - 2)\).

1. Then, calculate the differences in \(x\) and \(y\) coordinates:

• Calculate \(x_2 - x_1\):
• \(x_2 - x_1=3 - 2 = 1\).
• Calculate \(y_2 - y_1\):
• \(y_2 - y_1=-2 - 1=-3\).

1. Next, substitute into the distance formula:

• Substitute \(x_2 - x_1 = 1\) and \(y_2 - y_1=-3\) into \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
• \(d=\sqrt{(1)^2+(-3)^2}=\sqrt{1 + 9}=\sqrt{10}\).

Answer:

\(\sqrt{10}\)