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 \\(\square\\) units.
(simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Apply the distance formula

$$ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} $$

$$ d = \sqrt{(6 - 0)^2 + (2 - (-4))^2} $$

Simplify the radicand

$$ d = \sqrt{6^2 + 6^2} = \sqrt{36 + 36} = \sqrt{72} $$

Simplify the radical expression

$$ d = \sqrt{36 \times 2} = 6\sqrt{2} $$

Answer:

The distance between the given points is <blank>\(6\sqrt{2}\)</blank> units.
(Simplify your answer. Type an exact answer, using radicals as needed.)