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 15 units.
(simplify your answer. type an exact answer, using radicals as needed.)
the approximate distance between the pair of points (3,2) and (15,11) 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 \(x_1 = 3,y_1 = 2,x_2=15,y_2 = 11\).

Step2: Calculate the differences

First, find \(x_2 - x_1\) and \(y_2 - y_1\). \(x_2 - x_1=15 - 3=12\), \(y_2 - y_1=11 - 2 = 9\).

Step3: Substitute into the formula

Substitute into the distance formula: \(d=\sqrt{12^{2}+9^{2}}=\sqrt{144 + 81}=\sqrt{225}=15\) (exact value).

Step4: Approximate (if needed, but here exact value is already an integer)

Since \(15\) is an integer, when rounded to three decimal places, \(15.000\).

Answer:

The approximate distance is \(15.000\) units.