Question

nd the distance between the pair of points.
(8,10) and (17,22)

the distance between the points is
units.
simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(8,10)\) and \((x_2,y_2)=(17,22)\)

Step2: Use the distance formula

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
Substitute the values: \(d=\sqrt{(17 - 8)^2+(22 - 10)^2}\)

Step3: Calculate the differences

\(17-8 = 9\) and \(22 - 10=12\)
So \(d=\sqrt{9^2+12^2}\)

Step4: Calculate the squares

\(9^2 = 81\) and \(12^2=144\)
Then \(d=\sqrt{81 + 144}\)

Step5: Sum and simplify

\(81+144=225\), so \(d=\sqrt{225}\)
\(\sqrt{225}=15\)

Answer:

15