Select The Correct Answer.Which Equation Represents The Vertical Line Passing Through \[$(14, -16)\$\]?A. \[$x = -16\$\] B. \[$y = -16\$\] C. \[$x = 14\$\] D. \[$y = 14\$\]
Introduction
In coordinate geometry, a vertical line is a line that extends infinitely in one direction, parallel to the y-axis. It is characterized by a constant x-coordinate, while the y-coordinate can vary. In this article, we will explore how to represent a vertical line passing through a given point in the coordinate plane.
What is a Vertical Line?
A vertical line is a line that has a constant x-coordinate. This means that for any point on the line, the x-coordinate remains the same, while the y-coordinate can change. In other words, a vertical line is a line that extends infinitely in one direction, parallel to the y-axis.
Equation of a Vertical Line
The equation of a vertical line is given by:
x = a
where 'a' is the constant x-coordinate of the line. This equation represents a vertical line that passes through the point (a, y), where y can be any real number.
Selecting the Correct Answer
Now, let's consider the given options:
A. x = -16 B. y = -16 C. x = 14 D. y = 14
To select the correct answer, we need to identify the equation that represents a vertical line passing through the point (14, -16).
Analyzing the Options
Option A: x = -16
This equation represents a vertical line that passes through the point (-16, y), where y can be any real number. However, this is not the correct answer, as the point (14, -16) does not lie on this line.
Option B: y = -16
This equation represents a horizontal line that passes through the point (x, -16), where x can be any real number. This is not a vertical line, so it is not the correct answer.
Option C: x = 14
This equation represents a vertical line that passes through the point (14, y), where y can be any real number. This is the correct answer, as the point (14, -16) lies on this line.
Option D: y = 14
This equation represents a horizontal line that passes through the point (x, 14), where x can be any real number. This is not a vertical line, so it is not the correct answer.
Conclusion
In conclusion, the correct answer is C. x = 14, as it represents a vertical line passing through the point (14, -16).
Key Takeaways
- A vertical line is a line that extends infinitely in one direction, parallel to the y-axis.
- The equation of a vertical line is given by x = a, where 'a' is the constant x-coordinate of the line.
- To select the correct answer, we need to identify the equation that represents a vertical line passing through the given point.
Practice Problems
- Which equation represents a vertical line passing through the point (8, 12)?
- Which equation represents a vertical line passing through the point (-2, 5)?
- Which equation represents a vertical line passing through the point (10, -3)?
Answer Key
- x = 8
- x = -2
- x = 10
Vertical Lines in Coordinate Geometry: Q&A =============================================
Introduction
In our previous article, we explored the concept of vertical lines in coordinate geometry and how to represent them using equations. In this article, we will answer some frequently asked questions about vertical lines to help you better understand this topic.
Q: What is the equation of a vertical line?
A: The equation of a vertical line is given by x = a, where 'a' is the constant x-coordinate of the line.
Q: How do I determine if a line is vertical or not?
A: To determine if a line is vertical or not, you need to check if the x-coordinate is constant. If the x-coordinate is constant, then the line is vertical.
Q: Can a vertical line have a negative x-coordinate?
A: Yes, a vertical line can have a negative x-coordinate. For example, the equation x = -5 represents a vertical line with a negative x-coordinate.
Q: Can a vertical line have a fractional x-coordinate?
A: Yes, a vertical line can have a fractional x-coordinate. For example, the equation x = 3/4 represents a vertical line with a fractional x-coordinate.
Q: How do I graph a vertical line?
A: To graph a vertical line, you need to plot a point on the line and then draw a line that extends infinitely in one direction, parallel to the y-axis.
Q: Can a vertical line intersect with a horizontal line?
A: Yes, a vertical line can intersect with a horizontal line. For example, the equation x = 2 represents a vertical line that intersects with the horizontal line y = 3.
Q: Can a vertical line be parallel to a horizontal line?
A: Yes, a vertical line can be parallel to a horizontal line. For example, the equation x = 2 represents a vertical line that is parallel to the horizontal line y = 3.
Q: Can a vertical line have a slope?
A: No, a vertical line does not have a slope. The slope of a line is defined as the ratio of the change in y to the change in x, and for a vertical line, the change in x is zero.
Q: Can a vertical line be represented by a linear equation?
A: Yes, a vertical line can be represented by a linear equation. For example, the equation x = 2 represents a vertical line that can be written in the form y = mx + b, where m = 0 and b = 2.
Conclusion
In conclusion, vertical lines are an important concept in coordinate geometry, and understanding how to represent them using equations is crucial for solving problems in mathematics and science. We hope that this Q&A article has helped you better understand the concept of vertical lines and how to apply it to solve problems.
Practice Problems
- What is the equation of a vertical line that passes through the point (5, 2)?
- Is the line x = 3 a vertical line? Why or why not?
- Can a vertical line have a negative y-coordinate? Why or why not?
Answer Key
- x = 5
- Yes, the line x = 3 is a vertical line because the x-coordinate is constant.
- No, a vertical line cannot have a negative y-coordinate because the y-coordinate is not defined for a vertical line.