Structure of the Plane
Points that lie exactly on the axes.
Click to zoom
Points lying exactly on the horizontal and vertical axes.
, the origin , , , and
Plot points using (x, y), and work out which quadrant each one is in.
Preview · progress not saved — Chapter 1 is free
The x-axis, the y-axis, the origin, and what (x, y) means.
The 2-D Cartesian Coordinate System is a structured framework that allows us to use numbers to describe the exact physical location of points in a two-dimensional space.
Think of it as two number lines intersecting at a right angle.
Points that lie exactly on the axes.
Points lying exactly on the horizontal and vertical axes.
, the origin , , , and
Worked example: the coordinates of points B and G.
Problem. Based on the coordinate plane structure, determine the exact coordinates for points and strictly from their distance and direction relative to the origin .
Your turn: find the coordinates of point E.
Let us find the coordinates for point E based on its position on the Cartesian plane. We are given that point E is located 2.9 units to the left of the origin on the horizontal axis. Since it is on the left side of the origin along the x-axis, its x-coordinate must be negative, making it . Because the point lies directly on the x-axis, it has no vertical displacement from the origin. This means its y-coordinate is exactly . To write this as a standard coordinate pair, we place the x-coordinate first and the y-coordinate second. Therefore, the final coordinate notation for point E is .
The signs of x and y in each of the four quadrants.
x is negative
y is positive
x is positive
y is positive
x is negative
y is negative
x is positive
y is negative
Questions on what the x and y coordinates tell you.
What are the exact coordinates of a point that lies strictly on the y-axis, located 5 units below the origin?