Plot points on the 2D Cartesian plane using (x, y) coordinates and map them to their corresponding quadrants.
Define x-axis, y-axis, origin, and Cartesian coordinates.
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.
Graph showing points on axes and quadrants.
Points lying exactly on the horizontal and vertical axes.
, the origin , , , and
Worked example extracting coordinates for points B, G, and H.
Problem. Based on the coordinate plane structure, determine the exact coordinates for points and strictly from their distance and direction relative to the origin .
Faded example for plotting a point on an axis.
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 .
Matrix explaining the sign conventions for 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
MCQ testing the conceptual properties of x and y coordinates.
What are the exact coordinates of a point that lies strictly on the y-axis, located 5 units below the origin?