Question

question

find the distance between the points \\((-4, 2)\\) and \\((2, -1)\\).

report your answer as a simplified radical.

provide your answer below:

Explanation:

Apply the distance formula

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

$$ d = \sqrt{(2 - (-4))^2 + (-1 - 2)^2} $$

Simplify the terms inside the radical

$$ d = \sqrt{(6)^2 + (-3)^2} $$

$$ d = \sqrt{36 + 9} $$

$$ d = \sqrt{45} $$

Simplify the radical expression

$$ d = \sqrt{9 \times 5} = 3\sqrt{5} $$

Answer:

Find the distance between the points \((-4, 2)\) and \((2, -1)\).

Report your answer as a simplified radical.

Provide your answer below:
<blank>\(3\sqrt{5}\)</blank>