Problem 96 - Introductory and Intermediate Algebra for College Students 4th

Question

Explain how to plot a point in the rectangular coordinate system. Give an example with your explanation.

Step-by-Step Solution

Answer

To plot a point in the rectangular coordinate system, first understand that any point can be represented by an ordered pair, e.g. (x, y), where x represents the horizontal distance from the origin and y represents the vertical distance. To plot this point, move x units along the x-axis and y units along the y-axis from the origin, then mark the point where you land.

Step 1: Understanding the Rectangular Coordinate System

A rectangular coordinate system is a two-dimensional graph with two axes: the horizontal x-axis and the vertical y-axis. The intersection of these axes is called the origin, represented by the point (0, 0). Any point in the system can be represented by an ordered pair of numbers, representing its position relative to the origin on the x and y axes.

Step 2: Determining the Point to Plot

The point to plot in the coordinate system will be an ordered pair in brackets: for example, (x, y). Each value in the ordered pair corresponds to the position along an axis: the first number for the x-axis and the second number for the y-axis.

Step 3: Plotting the Point

To plot the point, start at the origin. Move along the x-axis the amount of the first number in the ordered pair and then move along the y-axis by the amount of the second number. The place where you land is the point.

Step 4: Example

For example, to plot the point (3, 2), start at the origin, move 3 units to the right along the x-axis, and then move 2 units up along the y-axis. Plot a dot or a mark where you land. That is your point (3, 2).