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 10 units.
(simplify your answer. type an exact answer, using radicals as needed.)
the approximate distance between the pair of points (2,3) and (10,9) is □ units.
(simplify your answer. type an integer or decimal rounded to three decimal places 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 \(x_1 = 2,y_1=3,x_2 = 10,y_2 = 9\).

Step2: Substitute the values into the formula

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

Step3: Calculate the squares

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

Step4: Add the values inside the square - root

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

Step5: Simplify the square - root

\(\sqrt{100}=10\). As an approximate value (since \(10\) is an integer), when rounded to three decimal places, it is \(10.000\).

Answer:

10.000