Apply the Pythagorean Theorem to find the distance between two points in a coordinate system

What you'll learn

1. Construct a right triangle on the coordinate plane by drawing horizontal and vertical segments connecting two given points, identifying the horizontal leg, vertical leg, and hypotenuse
2. Compute the lengths of the horizontal and vertical legs using the absolute difference of coordinates: horizontal leg = |x_2 - x_1|, vertical leg = |y_2 - y_1|
3. Apply the Pythagorean Theorem (a^2 + b^2 = c^2) to the constructed right triangle to find the straight-line distance between two points
4. Find distances between points in all four quadrants, including pairs involving negative coordinates, and leave answers in exact (radical) form or approximate with a calculator as appropriate
5. Recognize when two points share an x-coordinate or a y-coordinate, and determine that the distance between such points is simply the absolute difference of the differing coordinates -- no right triangle is needed

Prerequisites

• Apply the Pythagorean Theorem to determine unknown side lengths in right triangles