Question

find the distance between the pair of points (2,2) and (8,10).
the exact distance between the pair of points (2,2) and (8,10) is □ units.
(simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Recall the distance formula

The distance formula between two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\). Here, \(x_1 = 2,y_1 = 2,x_2 = 8,y_2 = 10\).

Step2: Substitute the values into the formula

Substitute the values: \((x_2 - x_1)=8 - 2=6\) and \((y_2 - y_1)=10 - 2 = 8\). Then \(d=\sqrt{(6)^2+(8)^2}\).

Step3: Calculate the squares

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

Step4: Add the values inside the square - root

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

Step5: Simplify the square - root

\(\sqrt{100}=10\).

Answer:

\(10\)