The Pythagorean theorem meets coordinate geometry
Measuring distances on a map, finding how far apart two cities are, calculating the length of a diagonal — these all come down to one formula. How far apart are two points on a graph? The distance formula d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} tells you — and it's really just the Pythagorean theorem in disguise.
In this lesson, you'll start with two points, A(1, 2) and B(4, 6), connected by a blue line. A right triangle drawn underneath shows the horizontal leg (3) and vertical leg (4). By the Pythagorean theorem: 3² + 4² = 25, so d = 5.
You'll discover that the distance formula works for ANY two points — even when the answer isn't a nice whole number. By the end, you'll be comfortable finding the distance between any two points on a coordinate plane.