11.1 Use the rectangular coordinate system

Plot points on a rectangular coordinate system

Many maps, such as the Campus Map shown in [link] , use a grid system to identify locations. Do you see the numbers $1,2,3,$ and $4$ across the top and bottom of the map and the letters A, B, C, and D along the sides? Every location on the map can be identified by a number and a letter.

For example, the Student Center is in section 2B. It is located in the grid section above the number $2$ and next to the letter B. In which grid section is the Stadium? The Stadium is in section 4D.

Just as maps use a grid system to identify locations, a grid system is used in algebra to show a relationship between two variables in a rectangular coordinate system. To create a rectangular coordinate system, start with a horizontal number line. Show both positive and negative numbers as you did before, using a convenient scale unit. This horizontal number line is called the x -axis    .

Now, make a vertical number line passing through the $x\text{-axis}$ at $0.$ Put the positive numbers above $0$ and the negative numbers below $0.$ See [link] . This vertical line is called the y -axis    .

Vertical grid lines pass through the integers marked on the $x\text{-axis}.$ Horizontal grid lines pass through the integers marked on the $y\text{-axis}.$ The resulting grid is the rectangular coordinate system.

The rectangular coordinate system is also called the $x\text{-}y$ plane, the coordinate plane, or the Cartesian coordinate system (since it was developed by a mathematician named René Descartes.)

The $x\text{-axis}$ and the $y\text{-axis}$ form the rectangular coordinate system. These axes divide a plane into four areas, called quadrants    . The quadrants are identified by Roman numerals, beginning on the upper right and proceeding counterclockwise. See [link] .

In the rectangular coordinate system, every point is represented by an ordered pair    . The first number in the ordered pair is the x -coordinate of the point, and the second number is the y -coordinate of the point.