Question

current objective
use the distance formula to find the distance between two points

question
use the distance formula to find the distance between the points \\((10, -8)\\) and \\((-4, -10)\\).

(write your answer in exact form.)

provide your answer below:

Explanation:

Identify the coordinates and the distance formula

$$ (x_1, y_1) = (10, -8),\quad (x_2, y_2) = (-4, -10) $$

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

Substitute the coordinates into the formula

$$ d = \sqrt{(-4 - 10)^2 + (-10 - (-8))^2} $$

$$ d = \sqrt{(-14)^2 + (-2)^2} $$

Simplify the radical expression

$$ d = \sqrt{196 + 4} = \sqrt{200} $$

$$ d = \sqrt{100 \cdot 2} = 10\sqrt{2} $$

Answer:

Use the distance formula to find the distance between the points \((10, -8)\) and \((-4, -10)\).

(Write your answer in exact form.)

Provide your answer below:
<blank>\(10\sqrt{2}\)</blank>