Flashcard 9 - Next Generation Quantitative Reasoning, Algebra, and Statistics Flashcard Set for the ACCUPLACER Test

Pythagorean theorem:

\(c^2 = a^2 + b^2\)
where c is the hypotenuse of a right triangle, and a and b are the legs of the right triangle.

The distance formula relates two points through a right triangle, where the line connecting the two points is the hypotenuse, and the difference between the x and y values of the points represents the length of the right triangle’s legs.
It is written as:

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

It can be tedious to memorize the distance formula, but if you can remember how it is derived from the Pythagorean theorem, you can avoid having to remember it.