Question

find the distance between the two points in simplest radical form. (8,6) and (3,-6)

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(8,6)\) and \((x_2,y_2)=(3, - 6)\)

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

Substitute the values: \(d=\sqrt{(3 - 8)^2+(-6 - 6)^2}\)

Step3: Simplify the expressions inside the square root

\(3-8=-5\), \(-6 - 6=-12\)
\(d=\sqrt{(-5)^2+(-12)^2}=\sqrt{25 + 144}\)

Step4: Calculate the sum inside the square root

\(25+144 = 169\)
\(d=\sqrt{169}\)

Step5: Find the square root

\(d = 13\)

Answer:

\(13\)