Plot Points

The Cartesian coordinate system, also called the rectangular coordinate system, is based on a two-dimensional plane consisting of the [latex]x[/latex]-axis and the[latex]y[/latex]-axis. Perpendicular to each other, the axes divide the plane into four sections. Each section is called a quadrant; the quadrants are numbered counterclockwise as shown in the figure below.

The center of the plane is the point at which the two axes cross. It is known as the origin or point [latex]\left(0,0\right)[/latex].

Each point in the plane is identified by its x-coordinate, or horizontal displacement from the origin, and its y-coordinate, or vertical displacement from the origin. Together we write them as an ordered pair indicating the combined distance from the origin in the form [latex]\left(x,y\right)[/latex]. An ordered pair is also known as a coordinate pair because it consists of [latex]x[/latex] and [latex]y[/latex]-coordinates. For example, we can represent the point [latex]\left(3,-1\right)[/latex] in the plane by moving three units to the right of the origin in the horizontal direction and one unit down in the vertical direction.

Plot the points [latex]\left(-2,4\right)[/latex], [latex]\left(3,3\right)[/latex], and [latex]\left(0,-3\right)[/latex] in the coordinate plane.

Show Solution

To plot the point [latex]\left(-2,4\right)[/latex], begin at the origin. The [latex]x[/latex]-coordinate is [latex]–2[/latex], so move two units to the left. The [latex]y[/latex]-coordinate is [latex]4[/latex], so then move four units up in the positive [latex]y[/latex] direction. To plot the point [latex]\left(3,3\right)[/latex], begin again at the origin. The [latex]x[/latex]-coordinate is [latex]3[/latex], so move three units to the right. The [latex]y[/latex]-coordinate is also [latex]3[/latex], so move three units up in the positive [latex]y[/latex] direction. To plot the point [latex]\left(0,-3\right)[/latex], begin again at the origin. The [latex]x[/latex]-coordinate is [latex]0[/latex]. This tells us not to move in either direction along the [latex]x[/latex]-axis. The [latex]y[/latex]-coordinate is [latex]–3[/latex], so move three units down in the negative [latex]y[/latex] direction.

 

Analysis of the Solution Note that when either coordinate is zero, the point must be on an axis. If the [latex]x[/latex]-coordinate is zero, the point is on the [latex]y[/latex]-axis. If the [latex]y[/latex]-coordinate is zero, the point is on the [latex]x[/latex]-axis.