Question

find the distance between the pair of points (0, - 4) and (6,2). if necessary, express the answer in simplified radical form and then round to two decimal places. the distance between the given points is □ units. simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Step1: Identify the coordinates

Let \((x_1,y_1)=(0, - 4)\) and \((x_2,y_2)=(6,2)\)

Step2: Use the distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

Substitute the values: \(d=\sqrt{(6 - 0)^2+(2-(-4))^2}\)

Step3: Simplify the expression inside the square - root

First, calculate \((6 - 0)^2=6^2 = 36\) and \((2 + 4)^2=6^2=36\)
Then \(d=\sqrt{36 + 36}=\sqrt{72}\)

Step4: Simplify the radical

\(\sqrt{72}=\sqrt{36\times2}=6\sqrt{2}\)

Step5: Round to two decimal places

\(6\sqrt{2}\approx6\times1.414 = 8.484\approx8.48\)

Answer:

The exact distance is \(6\sqrt{2}\) units and the approximate distance is \(8.48\) units.