Question

find the distance between the pair of points. if necessary, express answers in simplified radical form and then round to two decimal places.
(1,8) and (13,17)
the distance between the points is □ units.
(simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(1,8)\) and \((x_2,y_2)=(13,17)\)

Step2: Use the distance formula

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
Substitute the values: \(d=\sqrt{(13 - 1)^2+(17 - 8)^2}\)

Step3: Simplify the expressions inside the square root

\(13-1 = 12\), \(17 - 8=9\)
So \(d=\sqrt{12^2+9^2}=\sqrt{144 + 81}\)

Step4: Add the numbers inside the square root

\(144+81 = 225\)
So \(d=\sqrt{225}\)

Step5: Calculate the square root

\(\sqrt{225}=15\)

Answer:

\(15\)