Coordinate geometry

Coordinate geometry represents geometric objects with coordinates and studies their properties through algebraic equations. It connects spatial relationships to numerical calculation.

Cartesian coordinate system: A system that locates points using signed distances along perpendicular axes. Its axes assign each point the numbers used in coordinate geometry.
Distance formula: A formula for the distance between two points, derived from the Pythagorean theorem. It converts the coordinate differences between points into geometric length.
Analytic geometry: The branch of mathematics that studies geometric figures through algebraic equations and coordinates. This broader name emphasizes the algebraic methods underlying coordinate geometry.
Synthetic geometry: The study of geometric figures through axioms and logical constructions rather than coordinate calculations. It establishes geometric results without translating figures into algebra.
Ordered pair: A pair of numbers whose order distinguishes one coordinate from another. A point in the plane is represented by an ordered pair of coordinates.
Midpoint formula: A formula that gives the point halfway between two points by averaging their coordinates. Coordinate averages locate the center of a segment.
Computer graphics: The creation and manipulation of images using computational methods. Graphics systems position objects and calculate their shapes with coordinates.
Euclidean geometry: The geometry of points, lines, planes, and spaces governed by Euclid's parallel postulate. Coordinate geometry is one method for studying the familiar geometry of Euclidean space.
Equation of a line: An algebraic equation whose solutions describe the points lying on a line. It is the basic example of an equation describing a geometric object.
Slope: A measure of a line's steepness, defined as vertical change divided by horizontal change. Coordinate differences determine a line's direction and whether two lines are parallel.

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