Distance Between Two Points — Cheat sheet

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The formula

$|AB| = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$ - Pythagoras with legs $|x_2 - x_1|$ and $|y_2 - y_1|$ . Subtraction order never matters.

Special cases

Situation	Shortcut
Distance to origin	$\sqrt{x^2 + y^2}$
Horizontal segment ( $y_1 = y_2$ )	$\\|x_2 - x_1\\|$
Vertical segment ( $x_1 = x_2$ )	$\\|y_2 - y_1\\|$

Unknown coordinate procedure

Set formula equal to the given distance, square both sides, isolate the squared binomial, take $\pm$ roots - expect two answers. Classic integer triangles to recognize: 3-4-5, 5-12-13, 8-15-17.