Question

find the distance between the pair of points (2,3) and (8,9). if necessary, express the answer in simplified radical form and then round to two decimal places. the distance between the given points is units. (simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(2,3)\) and \((x_2,y_2)=(8,9)\)

Step2: Use the distance formula

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
Substitute the values: \(d=\sqrt{(8 - 2)^2+(9 - 3)^2}\)

Step3: Simplify the expression inside the square root

\((8 - 2)^2=6^2 = 36\) and \((9 - 3)^2=6^2=36\)
So \(d=\sqrt{36 + 36}=\sqrt{72}\)

Step4: Simplify the radical

\(\sqrt{72}=\sqrt{36\times2}=6\sqrt{2}\)

Answer:

\(6\sqrt{2}\)