A Point Is 3 Units Right And 2 Units Up From The Origin Of The Cartesian Plane. The Coordinates Of The Point Are:A. $(2,3)$ B. $(3,2)$ C. $(3,-2)$ D. $(-3,2)$

by ADMIN 172 views

The Cartesian plane is a fundamental concept in mathematics, used to represent geometric shapes and relationships between points. In this article, we will explore the concept of a point's coordinates and how to determine them based on its position relative to the origin.

What are Coordinates?

Coordinates are the values that represent a point's position on the Cartesian plane. They are typically denoted as (x, y) and consist of two parts: the x-coordinate and the y-coordinate. The x-coordinate represents the point's horizontal position, while the y-coordinate represents its vertical position.

Determining Coordinates

To determine a point's coordinates, we need to know its position relative to the origin. The origin is the point where the x-axis and y-axis intersect, and it is represented by the coordinates (0, 0). In this case, we are given that a point is 3 units right and 2 units up from the origin.

Analyzing the Options

Let's analyze the options given:

A. $(2,3)$ B. $(3,2)$ C. $(3,-2)$ D. $(-3,2)$

To determine the correct coordinates, we need to consider the point's position relative to the origin. Since the point is 3 units right and 2 units up, we can start by analyzing the x-coordinate.

The X-Coordinate

The x-coordinate represents the point's horizontal position. Since the point is 3 units right from the origin, its x-coordinate must be greater than 0. Let's examine the options:

  • Option A: $(2,3)$ - The x-coordinate is 2, which is less than 3. This option is incorrect.
  • Option B: $(3,2)$ - The x-coordinate is 3, which matches the given information. This option is a strong candidate.
  • Option C: $(3,-2)$ - The x-coordinate is 3, but the y-coordinate is negative. This option is incorrect.
  • Option D: $(-3,2)$ - The x-coordinate is negative, which does not match the given information. This option is incorrect.

The Y-Coordinate

The y-coordinate represents the point's vertical position. Since the point is 2 units up from the origin, its y-coordinate must be greater than 0. Let's examine the options:

  • Option A: $(2,3)$ - The y-coordinate is 3, which matches the given information.
  • Option B: $(3,2)$ - The y-coordinate is 2, which is less than 3. This option is incorrect.
  • Option C: $(3,-2)$ - The y-coordinate is negative, which does not match the given information. This option is incorrect.
  • Option D: $(-3,2)$ - The y-coordinate is 2, but the x-coordinate is negative. This option is incorrect.

Conclusion

Based on the analysis, the correct coordinates for the point are:

  • Option A: $(2,3)$

This option matches both the x-coordinate and the y-coordinate, making it the correct answer.

In conclusion, determining a point's coordinates based on its position relative to the origin requires a clear understanding of the Cartesian plane. By analyzing the x-coordinate and the y-coordinate, we can determine the correct coordinates for a point. In this case, the correct coordinates for the point are $(2,3)$.

Key Takeaways

  • Coordinates are the values that represent a point's position on the Cartesian plane.
  • The x-coordinate represents the point's horizontal position, while the y-coordinate represents its vertical position.
  • To determine a point's coordinates, we need to know its position relative to the origin.
  • Analyzing the x-coordinate and the y-coordinate can help us determine the correct coordinates for a point.

Further Reading

For more information on the Cartesian plane and coordinates, we recommend the following resources:

  • Khan Academy: Cartesian Plane
  • Math Is Fun: Cartesian Plane
  • Wolfram MathWorld: Cartesian Coordinate System

In our previous article, we explored the concept of a point's coordinates and how to determine them based on its position relative to the origin. We analyzed the options and determined that the correct coordinates for the point are $(2,3)$.

Q&A Session

We received many questions from our readers regarding the Cartesian plane and coordinates. Here are some of the most frequently asked questions and their answers:

Q: What is the Cartesian plane?

A: The Cartesian plane is a fundamental concept in mathematics, used to represent geometric shapes and relationships between points. It is a two-dimensional coordinate system that consists of an x-axis and a y-axis.

Q: What are coordinates?

A: Coordinates are the values that represent a point's position on the Cartesian plane. They are typically denoted as (x, y) and consist of two parts: the x-coordinate and the y-coordinate.

Q: How do I determine a point's coordinates?

A: To determine a point's coordinates, you need to know its position relative to the origin. The origin is the point where the x-axis and y-axis intersect, and it is represented by the coordinates (0, 0).

Q: What is the x-coordinate?

A: The x-coordinate represents the point's horizontal position. It is the value that tells you how far to the right or left the point is from the origin.

Q: What is the y-coordinate?

A: The y-coordinate represents the point's vertical position. It is the value that tells you how far up or down the point is from the origin.

Q: How do I analyze the x-coordinate and y-coordinate to determine a point's coordinates?

A: To analyze the x-coordinate and y-coordinate, you need to consider the point's position relative to the origin. If the point is to the right of the origin, its x-coordinate will be positive. If the point is to the left of the origin, its x-coordinate will be negative. Similarly, if the point is above the origin, its y-coordinate will be positive. If the point is below the origin, its y-coordinate will be negative.

Q: What are some common mistakes to avoid when determining a point's coordinates?

A: Some common mistakes to avoid when determining a point's coordinates include:

  • Not considering the point's position relative to the origin.
  • Not analyzing the x-coordinate and y-coordinate correctly.
  • Not using the correct units (e.g., inches, feet, etc.).

Q: How can I practice determining a point's coordinates?

A: You can practice determining a point's coordinates by using online resources, such as interactive graphs and coordinate planes. You can also try solving problems and exercises that involve determining coordinates.

Conclusion

Determining a point's coordinates based on its position relative to the origin requires a clear understanding of the Cartesian plane and coordinates. By analyzing the x-coordinate and y-coordinate, you can determine the correct coordinates for a point. We hope this Q&A session has helped you understand the concept of coordinates and how to determine them.

Key Takeaways

  • The Cartesian plane is a fundamental concept in mathematics used to represent geometric shapes and relationships between points.
  • Coordinates are the values that represent a point's position on the Cartesian plane.
  • To determine a point's coordinates, you need to know its position relative to the origin.
  • Analyzing the x-coordinate and y-coordinate can help you determine the correct coordinates for a point.

Further Reading

For more information on the Cartesian plane and coordinates, we recommend the following resources:

  • Khan Academy: Cartesian Plane
  • Math Is Fun: Cartesian Plane
  • Wolfram MathWorld: Cartesian Coordinate System

By understanding the Cartesian plane and coordinates, you can gain a deeper appreciation for the mathematics behind geometric shapes and relationships.