Coordinate Geometry Formulas
Points, lines, and circles on the x-y plane. These formulas turn coordinates into lengths, slopes, and equations.
Last updated: June 12, 2026
Coordinate geometry (also called analytic geometry) describes figures using ordered pairs instead of compass-and-straightedge construction. In a typical algebra or geometry course, you will use four core ideas on the plane: how far apart two points are (distance), where the center of a segment is (midpoint), how steep a line is (slope), and how to write the equation of a line or circle.
Almost every formula in this section comes back to the Pythagorean theorem. The distance formula is the most direct example: the horizontal and vertical gaps between two points form the legs of a right triangle, and the segment joining the points is the hypotenuse. Once you are comfortable with distance, midpoint and slope feel like natural next steps on the same grid.
On the SAT and ACT, coordinate geometry shows up in questions about side lengths, right triangles, and circles in standard form. Getting fast with the distance formula saves time when you need to compare three side lengths or find a radius from a center and a point on the circle.