Problem 21 - Introductory and Intermediate Algebra for College Students 4th

Question

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

Step-by-Step Solution

Answer

The point (0,0) is plotted at the intersection of the x-axis and y-axis, which is the origin of the coordinate system.

Step 1: Understanding Rectangular Coordinate System

In a rectangular coordinate system, we have two axes that are perpendicular to each other - the x-axis (horizontal) and the y-axis (vertical). Together, they form a grid where any point can be located using a pair of coordinates: (x, y). The first number indicates the x-coordinate (horizontal position, left or right from the central point, called the origin), while the second number indicates the y-coordinate (vertical position, up or down from the origin).

Step 2: Identify the Co-ordinates

The coordinates given are (0, 0). The first number 0 is the x-coordinate and the second number 0 is the y-coordinate. This means our point is neither left nor right on the x-axis, and neither up nor down on the y-axis. So, the point (0,0) lies at the intersection of x-axis and y-axis.

Step 3: Plotting the Point

Plot the point (0, 0) at the origin of the rectangular coordinate system. This is where the x-axis and y-axis cross each other. Therefore, (0, 0) is the point at which the x-axis and y-axis intersect.

Key Concepts

X-axis

The x-axis is one of the two fundamental axes in a rectangular coordinate system. It runs horizontally and is usually placed from left to right. When you look at a graph, the x-axis represents the horizontal line where the number increases as you move to the right and decreases as you move to the left. Each point on this line has a unique x-coordinate value. For example, in the coordinate (3, 2), the number 3 represents the x-coordinate, indicating a position three units to the right of the vertical y-axis.

The x-axis serves as a reference line for determining horizontal distances. Understanding the x-axis is crucial for identifying the position of points and creating accurate graphs.

• Horizontal line
• Used to determine positions left or right
• Intersects the y-axis at the origin

Y-axis

The y-axis is the second fundamental component of a rectangular coordinate system, aligning vertically from top to bottom. When you observe a graph, the y-axis runs straight up and down. It helps you understand vertical positioning. The number increases as you move upwards and decreases as you move downwards relative to the origin. In the coordinate pair (3, 2), the number 2 represents the y-coordinate. This shows a position two units up from the horizontal x-axis.

Recognizing the y-axis's role is vital in pinpointing a point’s vertical alignment. It also complements the x-axis to give a complete picture of a point's location. Together, they create a grid that assists in mapping and understanding complex data.

• Vertical line
• Determines positioning up or down
• Essential in forming the coordinate grid

Origin

The origin is a special point where the x-axis and y-axis intersect in a rectangular coordinate system. It is denoted as (0,0), meaning its position is zero units from the x-axis and zero units from the y-axis. Essentially, it's the starting point for measuring coordinates and acts as a central point of reference.

When plotting points, the origin serves as a baseline. It’s where measurements begin, whether you are moving to the right, left, up, or down. Visualizing the origin is crucial as it helps align all points correctly. For example, if you need to plot a point at (0,0), it remains at the origin, signifying no shift away from this central point. Understanding the origin helps ensure that graphs are precise and interpret data accurately.

• Intersection of x-axis and y-axis
• Coordinates: (0,0)
• Foundation for plotting points