Question

find the distance between the two points in simplest radical form

Explanation:

Step1: Identify the coordinates of the two points

Let the two points be \(A(-7,1)\) and \(B(-3,8)\).

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

Here \(x_1=-7,y_1 = 1,x_2=-3,y_2 = 8\).
First, calculate \((x_2 - x_1)\) and \((y_2 - y_1)\):
\(x_2 - x_1=-3-(-7)=-3 + 7=4\)
\(y_2 - y_1=8 - 1=7\)
Then, substitute into the formula:
\(d=\sqrt{(4)^2+(7)^2}=\sqrt{16 + 49}\)

Step3: Simplify the expression

\(d=\sqrt{65}\)

Answer:

\(\sqrt{65}\)