Question

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

Explanation:

Step1: Identify the coordinates of the two points

Let the first point be \((x_1,y_1)=(-1,4)\) and the second point be \((x_2,y_2)=(6,-8)\)

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

Substitute the values: \(d=\sqrt{(6-(-1))^2+(-8 - 4)^2}\)

Step3: Simplify the expressions inside the square root

\(6-(-1)=6 + 1=7\) and \(-8-4=-12\)
So \(d=\sqrt{7^2+(-12)^2}=\sqrt{49 + 144}\)

Step4: Add the numbers inside the square root

\(49+144 = 193\)
So \(d=\sqrt{193}\)

Answer:

\(\sqrt{193}\)