1.29 Coordinate Plane Definitions

Coordinate Plane Definitions establishes the vocabulary for the two-dimensional grid used to represent pairs of related numerical values as points in space, describing the paired notation used to locate a point, the two directional components that make up that notation, the fixed reference point from which every location is measured, the two perpendicular reference lines that structure the plane, and the four regions those lines divide the plane into.

Coordinate Plane

The coordinate plane is a flat, two-dimensional surface formed by two perpendicular number lines, used to represent the relationship between two variables by assigning each pair of related values a unique location. Every point within the coordinate plane corresponds to exactly one pair of numerical values, and every pair of numerical values corresponds to exactly one point, establishing a complete one-to-one correspondence between numbers and positions.

Ordered Pair

An ordered pair is a set of two numbers written in a fixed sequence, enclosed in parentheses and separated by a comma, used to specify a single point's location on the coordinate plane, such as (4, 3). The order in which the two numbers are written is meaningful: the ordered pair (4, 3) designates a different point than the ordered pair (3, 4), even though both use the same two numbers.

Horizontal Coordinate

The horizontal coordinate is the first number in an ordered pair, indicating how far to the right (if positive) or left (if negative) a point lies from the fixed reference point of the plane, measured along the horizontal direction. In the ordered pair (4, 3), the horizontal coordinate is 4.

Vertical Coordinate

The vertical coordinate is the second number in an ordered pair, indicating how far up (if positive) or down (if negative) a point lies from the fixed reference point of the plane, measured along the vertical direction. In the ordered pair (4, 3), the vertical coordinate is 3.

Coordinate Origin

The coordinate origin is the single fixed point on the coordinate plane where the horizontal and vertical reference lines intersect, corresponding to the ordered pair (0, 0), from which every other point's horizontal and vertical coordinates are measured.

Coordinate Axis

A coordinate axis is one of the two perpendicular reference lines that structure the coordinate plane and intersect at the origin: the horizontal axis, extending left and right, and the vertical axis, extending up and down. Every point's location is described in terms of its distance from these two axes, expressed through its horizontal and vertical coordinates.

Quadrant

A quadrant is one of the four regions into which the coordinate plane is divided by its two perpendicular axes, each region distinguished by a specific combination of positive and negative coordinate signs. The quadrant containing points with both coordinates positive is conventionally numbered first, and the remaining three quadrants are numbered in order proceeding counterclockwise around the origin, each corresponding to a different combination of positive and negative horizontal and vertical coordinates.

Together, these definitions establish the coordinate plane as a structured grid built from two perpendicular axes meeting at the origin, divided into four quadrants, on which any pair of related numerical values can be located precisely and uniquely using an ordered pair composed of a horizontal and a vertical coordinate.