Geometry Basic Elements:  

A lot of the geometric shapes and figures you have learned thus far will eventually have formulas assigned to them as you delve into the world of algebra and more advanced geometry. In order for those formulas to make physical, geometric sense, they need to be placed in what is called a coordinate plane. In this lesson, we will learn the properties of the coordinate plane and how to graph points on it. 

Properties of the Coordinate Plane 

To the right is the Cartesian coordinate plane. Because we are not going to be using any other coordinate plane in the near future, and it is the standard coordinate plane for math students all around the world, we will call it simply the Coordinate Plane. X 

The thick black lines are called the “axes” (plural of the word axis). The horizontal – right-to-left – axis is called the “x axis”, as indicated by the x to the left of the coordinate plane. The vertical – up-to-down – axis is called the “y axis”, as indicated by the y directly above the coordinate plane. The arrows indicate that the axes go on to infinity. 

The numbers along each axis are values a point can have: x-values and y-values. As you go farther to the right, the x-values increase in the positive direction, and as you go farther to the left, the x-values decrease in the negative direction. Similarly, as you go up, the y-values increase in the positive direction, and as you go down, the y-values decrease in the negative direction. 

There are four quadrants to the Coordinate Plane: I, II, III, and IV, the Roman numerals for 1, 2, 3, and 4. They are color-coded and labeled on the Coordinate Plane above. 

Lastly, any point on the Coordinate Plane is defined by what is called an “ordered pair” enclosed in parentheses like this: (x,y). The x-value always comes first. For example, the orange point in Quadrant II has an ordered pair of (-3,4). 

Example: 

Plot the points defined by the following ordered pairs: 

(2, 3) 

(-4, -4) 

(-1, -3) 

(4, 0) 

Solution: 

Line 

Ray