Calculating the Distance of a Point from the Y-Axis: A Comprehensive Guide

Understanding the distance of a point from the y-axis is a fundamental concept in coordinate geometry. This guide will explore the concept, provide clear explanations, and offer practical examples to help you grasp this topic thoroughly.

Introduction to Coordinates and the Y-Axis

In a two-dimensional Cartesian coordinate system, every point is defined by its coordinates: (x-coordinate, y-coordinate). The y-axis is the vertical line that runs through the origin (0,0) and is the reference line for the y-coordinate values.

Distance from the Y-Axis

The distance of a point from the y-axis is simply the absolute value of its x-coordinate. This means that if you have a point with coordinates (a, b), the distance from the y-axis is the absolute value of 'a', denoted as |a|.

Example: Distance of the Point (7, -2) from the Y-Axis

For the point (7, -2), the x-coordinate is 7. Therefore, the distance from the y-axis is:

Distance |7| 7

So, the distance of the point (7, -2) from the y-axis is 7 units.

General Formula for Distance from a Line

While the distance from the y-axis can be directly determined from the x-coordinate, understanding the formula to calculate the distance from any other line is essential for broader applications of coordinate geometry.

The distance from a point (x1, y1) to a vertical line x c is given by the formula:

d |x1 - c|

For the point (7, -2) and the line x 0 (the y-axis), the distance is:

d |7 - 0| 7

Additional Considerations

It's important to note that the concept of distance is not limited to just the y-axis. The distance from a point to a line can be calculated using the formula:

d |Ax1 By1 C| / √(A^2 B^2)

For instance, if we consider the point (7, -8) and the line x 0, the distance is:

d |1 * 7 0 * (-8) 0| / √(1^2 0^2) 7 / 1 7

Conclusion

Understanding the basics of the distance from the y-axis is crucial for solving more complex problems in coordinate geometry. Whether you are dealing with simple points or more complex lines, the key concept remains the x-coordinate. This guide has provided clear explanations and examples to help you grasp this fundamental concept.

References

For a deeper exploration of coordinate geometry, consider the following resources:

Math Is Fun - Systems of Linear Equations Khan Academy - Coordinate Geometry Math Planet - Distance Between Two Points and the Midpoint Formula