Functions: Coordinate System

The grid is built from two intersecting axes:

• x-axis: The horizontal axis. Its values increase as you move right (positive direction) and decrease as you move left (negative direction).
• y-axis: The vertical axis. Its values increase as you move upwards (positive direction) and decrease as you move downwards (negative direction).
• Intersection: The two axes cross each other at a 90° angle (they are perpendicular). The point where they cross is called the origin, represented by coordinates $(0, 0)$.

Any point on the coordinate plane is represented as an ordered pair written in the format:

• The first number ($x$) is the x-coordinate (abscissa). It tells you how many units to move horizontally from the origin (right if positive, left if negative).
• The second number ($y$) is the y-coordinate (ordinate). It tells you how many units to move vertically from the origin (up if positive, down if negative).

The two crossing axes divide the coordinate system into four regions called quadrants, numbered counter-clockwise starting from the top-right:

• First Quadrant (I): Top-right region. Both $x$ and $y$ are positive ($x > 0, y > 0$). Example: $(2, 3)$.
• Second Quadrant (II): Top-left region. $x$ is negative and $y$ is positive ($x < 0, y > 0$). Example: $(-4, 1)$.
• Third Quadrant (III): Bottom-left region. Both $x$ and $y$ are negative ($x < 0, y < 0$). Example: $(-2, -3)$.
• Fourth Quadrant (IV): Bottom-right region. $x$ is positive and $y$ is negative ($x > 0, y < 0$). Example: $(3, -5)$.

Note: Points that lie directly on the x-axis or y-axis (like $(0, 4)$ or $(-3, 0)$) or at the origin $(0, 0)$ are not located in any of the four quadrants.