Question

find the distance between the pair of points.

\\((12,23)\\) and \\((-3,-10)\\)

the distance is \\(\square\\).
(round to the nearest thousandth as needed.)

Explanation:

Identify the given coordinates

Using the Coordinate Distance knowledge point

$$ (x_1, y_1) = (12, 23) $$

$$ (x_2, y_2) = (-3, -10) $$

Apply the distance formula

Using the Distance Formula knowledge point

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

$$ d = \sqrt{(-3 - 12)^2 + (-10 - 23)^2} $$

Simplify the differences

Using the Distance Formula knowledge point

$$ d = \sqrt{(-15)^2 + (-33)^2} $$

$$ d = \sqrt{225 + 1089} $$

Calculate the final distance

Using the Distance Formula knowledge point

$$ d = \sqrt{1314} \approx 36.2491379 $$

$$ d \approx 36.249 $$

Answer:

Find the distance between the pair of points.

\((12,23)\) and \((-3,-10)\)

The distance is <blank>36.249</blank>.
(Round to the nearest thousandth as needed.)