Question

find the distance between the pair of points (2,3) and (10,9).
the exact distance between the pair of points (2,3) and (10,9) 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 \((x_2,y_2)=(10,9)\)

Step2: Use the distance formula

The distance formula is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)
Substitute the values: \(d=\sqrt{(10 - 2)^2+(9 - 3)^2}\)

Step3: Calculate the differences

\(10-2 = 8\) and \(9 - 3=6\)
So \(d=\sqrt{8^2+6^2}\)

Step4: Calculate the squares

\(8^2=64\) and \(6^2 = 36\)
Then \(d=\sqrt{64 + 36}\)

Step5: Add the values inside the radical

\(64+36=100\)
So \(d=\sqrt{100}\)

Step6: Simplify the radical

\(\sqrt{100}=10\)

Answer:

$10$