Question

find the distance between the pair of points. if necessary, express answers in simplified radical form and then round to two decimal places.
(8,5) 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 \((x_1,y_1)=(8,5)\) and \((x_2,y_2)=(13,17)\)

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

Substitute the values: \(d=\sqrt{(13 - 8)^2+(17 - 5)^2}\)

Step3: Calculate the differences

\(13-8 = 5\) and \(17 - 5=12\)
So \(d=\sqrt{5^2+12^2}\)

Step4: Calculate the squares

\(5^2 = 25\) and \(12^2=144\)
Then \(d=\sqrt{25 + 144}\)

Step5: Add the values inside the square - root

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

Step6: Simplify the square - root

\(\sqrt{169}=13\)

Answer:

\(13\)