The Coordinate Plane Study Guide

Updated on Oct 3, 2011

Introduction to The Coordinate Plane

Geometry is just plane fun!

—Author Unknown

This lesson welcomes you into the world of coordinate geometry and teaches you the key terms involved.

In the 1600S, René Descartes, a philosopher and mathematician, created a method of positioning a point in a plane by its distance, x and y, from the intersection of two fixed lines drawn at right angles in the plane. This plane came to be called the Cartesian plane, or simply, the coordinate plane.

A coordinate plane is used to plot or locate points in a plane. The horizontal axis is called the x-axis, and the vertical axis is called the y-axis.

The Coordinate Plane

There are four quadrants created by the intersection of the x- and y-axes. The quadrants are named by Roman numerals; quadrant I is in the upper right corner. The other quadrants follow in a counterclockwise direction. The intersection of the axes is called the origin.

The Coordinate Plane

Notice the signs of the ordered pairs and where they lie in the coordinate plane:

      In quadrant I, all points have the sign (+x, +y).
      In quadrant II, all points have the sign (–x, +y).
      In quadrant III, all points have the sign (–x, –y).
      In quadrant IV, all points have the sign (+x, –y).

It is easy to plot points on the coordinate grid. Points are given as ordered pairs, which are just x/y pairs. An ordered pair is always written (x,y). You simply go left or right along the x-axis to find your x, and then you go up or down to the appropriate y-coordinate. The y-coordinate is always named second. The x-coordinate is the horizontal distance from the origin. Positive x-coordinates are to the right of the origin and negative x-coordinates are to the left of the origin. The y-coordinate is the vertical distance from the origin. Positive y-coordinates are above the origin and negative y-coordinates are below the origin. Each point has a unique location, as defined by its ordered pair. The coordinates for the origin are (0,0).

The following graph is an example of the coordinate plane.

The Coordinate Plane

Look at the point labeled E, with the coordinates (2,3). The x-coordinate is listed first in the coordinate pair. The x value of a point is the distance from the y-axis to that point. Point E is two units from the y-axis, so its x value is 2. The y-coordinate is listed second in the coordinate pair. The y value of a point is the distance from the x-axis to that point. Point E is three units from the x-axis, so its y value is 3.

What are the coordinates of point G? Point G is –4 units from the y-axis and four units from the x-axis. The coordinates of point G are (–4,4).

Find practice problems and solutions at The Coordinate Plane Practice Questions.

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