Question

find the distance between the pair of points. if necessary, express answers in simplified radical form and then round to two decimal places.

(1, 5) and (5, 2)

the distance between the points is units.
(simplify your answer. type an exact answer, using radicals as needed.)

Explanation:

Identify the given coordinates

$$ (x_1, y_1) = (1, 5),\quad (x_2, y_2) = (5, 2) $$

Apply the distance formula

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

$$ d = \sqrt{(5 - 1)^2 + (2 - 5)^2} $$

$$ d = \sqrt{4^2 + (-3)^2} $$

Simplify the radical expression

$$ d = \sqrt{16 + 9} = \sqrt{25} = 5 $$

Answer:

The distance between the points is <blank>5</blank> units.
(Simplify your answer. Type an exact answer, using radicals as needed.)