The Cartesian Coordinate System
The Cartesian coordinate system is the standard grid for graphing in Grade 8 math (Yoshiwara Core Math). Two perpendicular number lines — horizontal x-axis and vertical y-axis — intersect at the origin (0, 0). Points are located by ordered pairs (x, y): move x units horizontally then y units vertically. The axes create four quadrants: I (+,+), II (−,+), III (−,−), IV (+,−). Named after René Descartes, this system bridges algebra and geometry, enabling equations to be graphed as visual lines and curves.
Key Concepts
Property To display the values of two variables, we use two number lines. The horizontal number line is called the $x$ axis, and the vertical number line is the $y$ axis. The point where the two axes intersect is called the origin. The two axes divide the plane into four regions called quadrants, numbered 1 through 4 counter clockwise around the origin.
Examples Points in Quadrant I, like $(4, 6)$, have a positive x coordinate (a move to the right) and a positive y coordinate (a move up). Points in Quadrant III, like $( 1, 5)$, have a negative x coordinate (a move to the left) and a negative y coordinate (a move down). The origin is the starting point $(0, 0)$ where the x axis and y axis meet.
Explanation Think of the Cartesian coordinate system as a map for numbers. It uses two perpendicular lines, the x axis (horizontal) and y axis (vertical), to give a unique address to any point on a flat surface, letting us visualize equations.
Common Questions
What is the Cartesian coordinate system?
A 2D grid of a horizontal x-axis and vertical y-axis intersecting at origin (0,0), used to locate points with ordered pairs (x,y).
How do you plot (−3, 4)?
Start at origin. Move 3 left (x = −3), then 4 up (y = 4). Mark the point.
What are the four quadrants?
I: (+,+) top-right. II: (−,+) top-left. III: (−,−) bottom-left. IV: (+,−) bottom-right.
What is the origin?
The point (0,0) where x-axis and y-axis intersect.
What is the difference between x and y coordinates?
x-coordinate (first number) = horizontal position. y-coordinate (second number) = vertical position.