Question

find the distance between the pair of points (3,2) and (15,11).
the exact distance between the pair of points (3,2) and (15,11) is units.
(simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(3,2)\) and \((x_2,y_2)=(15,11)\).

Step2: Use the distance formula

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\).
Substitute the values: \(d=\sqrt{(15 - 3)^2+(11 - 2)^2}\).

Step3: Calculate the differences

\(15-3 = 12\) and \(11 - 2=9\). So \(d=\sqrt{12^2+9^2}\).

Step4: Compute the squares

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

Step5: Add the numbers inside the square - root

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

Step6: Simplify the square - root

\(\sqrt{225}=15\).

Answer:

\(15\)