Point C Is Plotted At (-6,3). Point D Is Plotted At (6,3). Which Statements About The Relationship Between Point C And D Are True?

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Introduction

In mathematics, points on a coordinate plane are used to represent locations in a two-dimensional space. When dealing with points, it's essential to understand their relationships, including their positions, distances, and angles. In this article, we will explore the relationship between two points, C and D, which are plotted at (-6,3) and (6,3) respectively.

The Coordinate Plane

The coordinate plane is a two-dimensional space that uses a grid system to represent points. The x-axis represents the horizontal direction, while the y-axis represents the vertical direction. Each point on the plane is identified by its coordinates, which are represented as (x, y). In this case, point C is plotted at (-6,3), and point D is plotted at (6,3).

Relationship Between Points C and D

To understand the relationship between points C and D, we need to analyze their coordinates. Both points have the same y-coordinate, which is 3. This means that they lie on the same horizontal line. However, their x-coordinates are different, with point C having an x-coordinate of -6 and point D having an x-coordinate of 6.

Statements About the Relationship Between Points C and D

Based on the coordinates of points C and D, we can make the following statements about their relationship:

  • Points C and D are symmetric with respect to the y-axis: Since point C has an x-coordinate of -6 and point D has an x-coordinate of 6, they are equidistant from the y-axis. This means that they are symmetric with respect to the y-axis.
  • Points C and D lie on the same horizontal line: As mentioned earlier, both points have the same y-coordinate, which is 3. This means that they lie on the same horizontal line.
  • Points C and D are mirror images of each other: Since they are symmetric with respect to the y-axis and lie on the same horizontal line, points C and D are mirror images of each other.
  • The distance between points C and D is equal to the difference between their x-coordinates: The distance between two points on a coordinate plane can be calculated using the distance formula. In this case, the distance between points C and D is equal to the difference between their x-coordinates, which is 6 - (-6) = 12.

Conclusion

In conclusion, points C and D are symmetric with respect to the y-axis, lie on the same horizontal line, are mirror images of each other, and have a distance of 12 units between them. Understanding the relationship between points on a coordinate plane is essential in mathematics, and this article has provided a clear explanation of the relationship between points C and D.

Key Takeaways

  • Points on a coordinate plane can be represented by their coordinates.
  • The relationship between points can be analyzed by comparing their coordinates.
  • Points that have the same y-coordinate lie on the same horizontal line.
  • Points that are symmetric with respect to the y-axis are mirror images of each other.
  • The distance between two points can be calculated using the distance formula.

Further Reading

For further reading on the topic of coordinate geometry, we recommend the following resources:

References

Introduction

In our previous article, we explored the relationship between points C and D, which are plotted at (-6,3) and (6,3) respectively. We discussed how points C and D are symmetric with respect to the y-axis, lie on the same horizontal line, are mirror images of each other, and have a distance of 12 units between them. In this article, we will answer some frequently asked questions about the relationship between points C and D.

Q: What is the significance of the y-coordinate in the relationship between points C and D?

A: The y-coordinate is significant in the relationship between points C and D because it determines the horizontal line on which they lie. Since both points have the same y-coordinate, they are equidistant from the y-axis and lie on the same horizontal line.

Q: How do we determine the distance between points C and D?

A: The distance between points C and D can be calculated using the distance formula. The distance formula is given by:

d = √((x2 - x1)² + (y2 - y1)²)

where (x1, y1) and (x2, y2) are the coordinates of the two points. In this case, the distance between points C and D is equal to the difference between their x-coordinates, which is 6 - (-6) = 12.

Q: What is the relationship between points C and D in terms of symmetry?

A: Points C and D are symmetric with respect to the y-axis. This means that they are equidistant from the y-axis and are mirror images of each other.

Q: Can points C and D be considered as a pair of points that are collinear?

A: Yes, points C and D can be considered as a pair of points that are collinear. Since they lie on the same horizontal line, they are collinear.

Q: How do we determine the midpoint of the line segment joining points C and D?

A: The midpoint of the line segment joining points C and D can be calculated using the midpoint formula. The midpoint formula is given by:

M = ((x1 + x2)/2, (y1 + y2)/2)

where (x1, y1) and (x2, y2) are the coordinates of the two points. In this case, the midpoint of the line segment joining points C and D is ((-6 + 6)/2, (3 + 3)/2) = (0, 3).

Q: Can points C and D be considered as a pair of points that are diametrically opposite?

A: No, points C and D cannot be considered as a pair of points that are diametrically opposite. Diametrically opposite points are points that are equidistant from the center of a circle and are on opposite sides of the circle. In this case, points C and D are not diametrically opposite because they are not on opposite sides of a circle.

Conclusion

In conclusion, the relationship between points C and D is a fundamental concept in mathematics that is used to understand the properties of points on a coordinate plane. We hope that this Q&A article has provided a clear explanation of the relationship between points C and D and has helped to clarify any doubts that you may have had.

Key Takeaways

  • Points on a coordinate plane can be represented by their coordinates.
  • The relationship between points can be analyzed by comparing their coordinates.
  • Points that have the same y-coordinate lie on the same horizontal line.
  • Points that are symmetric with respect to the y-axis are mirror images of each other.
  • The distance between two points can be calculated using the distance formula.
  • The midpoint of a line segment can be calculated using the midpoint formula.

Further Reading

For further reading on the topic of coordinate geometry, we recommend the following resources:

References