Problem 15 - Introductory and Intermediate Algebra for College Students 4th

Question

Plot the given point in a rectangular coordinate system. $$(0,-3)$$

Step-by-Step Solution

Answer

The point (0, -3) is located directly below the origin (0, 0) on the y-axis at a distance of 3 units.

Step 1: Understand the coordinate system

A rectangular (or Cartesian) coordinate system is composed of two number lines that intersect at a right angle at their zero points. The horizontal line is referred to as the x-axis and the vertical line is known as the y-axis. Any point in this system is defined by an ordered pair of numbers (x, y). The first number, or x-coordinate, denotes the horizontal distance from the origin (0,0), while the second number, or y-coordinate, denotes the vertical distance from the origin.

Step 2: Identify the coordinates of the point

The point given in this exercise is (0, -3). The 0 represents the x-coordinate, meaning there is no movement along the x-axis, and -3 represents the y-coordinate, indicating a movement of 3 units downwards from the origin.

Step 3: Plot the point

Start at the origin, since the x-coordinate is 0, there is no need to move along the x-axis. Then move 3 units downwards along the y-axis due to the negative y-coordinate. This location in the coordinate system is the position of the point (0, -3). Mark this point.