**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*-axisThere 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**.

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.

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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