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 \((-1,-3)\) and \((4,5)\). Let \((x_1,y_1)=(-1,-3)\) and \((x_2,y_2)=(4,5)\).

Step2: Apply the distance formula

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
Substitute the values: \(x_2 - x_1=4-(-1)=4 + 1=5\), \(y_2 - y_1=5-(-3)=5 + 3=8\).
Then \(d=\sqrt{(5)^2+(8)^2}=\sqrt{25 + 64}\).

Step3: Simplify the expression

\(d=\sqrt{89}\).

Answer:

\(\sqrt{89}\)