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Chapter 4: Problem 53

Is the point (-3,0) on the \(x\) -axis or \(y\) -axis? How do

Short Answer

Expert verified
The point (-3, 0) is on the x-axis.

Step by step solution

01

Determine Coordinates

Identify the given coordinates of the point. The point provided is (-3, 0).
02

Check the X Coordinate

If a point is on the y-axis, its x-coordinate must be 0. Check if the x-coordinate of the given point is 0. Here, the x-coordinate is -3, so the point is not on the y-axis.
03

Check the Y Coordinate

If a point is on the x-axis, its y-coordinate must be 0. Check if the y-coordinate of the given point is 0. Here, the y-coordinate is 0, so the point is on the x-axis.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

x-axis
Understanding the concept of the x-axis is essential in coordinate geometry. The x-axis is the horizontal line in a coordinate plane. This axis runs left to right and is used to determine the horizontal position of a point.
The x-axis intersects the y-axis at zero, which is known as the origin \( (0,0) \). If a point lies on the x-axis, its y-coordinate will always be zero. For example, in the original exercise, the point \( (-3,0) \) has its y-coordinate as zero, indicating it lies on the x-axis.
y-axis
Now let's look at the y-axis. The y-axis is the vertical line in a coordinate plane. It runs up and down and is used to determine the vertical position of a point.
Similar to the x-axis, the y-axis also intersects the x-axis at the origin \( (0,0) \). If a point lies on the y-axis, its x-coordinate will always be zero. This is a good way to check the position of a point. For instance, if the point was (0,3), it would mean it lies on the y-axis because the x-coordinate is zero.
coordinate geometry
Coordinate geometry is a branch of mathematics that deals with points on the coordinate plane. In a coordinate plane, each point is represented by a pair of numerical coordinates \( (x,y) \). These coordinates are measured along the x-axis and y-axis.
Using coordinate geometry, we can identify the location, distance, and relationship between different points. It helps in solving various geometrical problems involving shapes, lines, distances, and angles. Being comfortable with both axes and how to interpret coordinates is crucial for mastering coordinate geometry.
identifying points
Identifying points on a coordinate plane is a fundamental skill in coordinate geometry. A point is defined by an ordered pair of numbers \( (x,y) \), where the first number corresponds to the horizontal position (x-coordinate) and the second to the vertical position (y-coordinate).
To identify if a point lies on an axis, you need to check its coordinates. For the x-axis, the y-coordinate must be zero, and for the y-axis, the x-coordinate must be zero.
  • In the given exercise, the point \( (-3,0) \) has a y-coordinate of 0, identifying it as lying on the x-axis.
  • If a point has coordinates \( (0,y) \), such as \( (0,-2) \), it lies on the y-axis.
This method helps in quickly locating and understanding the positions of points in a coordinate plane.

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