Rotating a Point Counterclockwise

Oct 13, 2025 by magicalceylontours.com 120 views

Introduction

Rotating a point in a coordinate plane involves a transformation that changes the position of the point while maintaining its distance from the origin. In this article, we will explore the process of rotating a point at ${$ (-4, 6)$}$ ${ $180^{\circ}\$}$ counterclockwise and determine the resulting point.

Understanding Rotation

Rotation is a type of transformation that involves rotating a point or an object around a fixed point called the center of rotation. The angle of rotation is measured in degrees, and the direction of rotation can be either clockwise or counterclockwise. In this case, we are rotating the point ${$ (-4, 6)$}$ ${ $180^{\circ}\$}$ counterclockwise.

Rotating a Point Counterclockwise

To rotate a point counterclockwise, we can use the following formula:

${(x', y') = (-x, -y)}$

where ${(x, y)}$ is the original point and ${(x', y')}$ is the rotated point.

Applying the Rotation Formula

Using the formula above, we can rotate the point ${$ (-4, 6)$}$ ${ $180^{\circ}\$}$ counterclockwise by substituting the values of ${x}$ and ${y}$ into the formula:

${(x', y') = (-(-4), -6)}$ ${(x', y') = (4, -6)}$

Determining the Resulting Point

Based on the calculation above, the resulting point after rotating ${$ (-4, 6)$}$ ${ $180^{\circ}\$}$ counterclockwise is ${$ (4, -6)$}$.

Conclusion

Discussion

The correct answer is ${$ (4, -6)$}$. This can be verified by using the rotation formula and substituting the values of ${x}$ and ${y}$ into the formula.

Step-by-Step Solution

Understand the concept of rotation and the formula for rotating a point counterclockwise.
Identify the original point and the angle of rotation.
Substitute the values of ${x}$ and ${y}$ into the rotation formula.
Calculate the resulting point using the formula.
Verify the answer by checking the options provided.

Common Mistakes

Failing to understand the concept of rotation and the formula for rotating a point counterclockwise.
Not identifying the original point and the angle of rotation correctly.
Not substituting the values of ${x}$ and ${y}$ into the rotation formula correctly.
Not calculating the resulting point using the formula correctly.

Tips and Tricks

Make sure to understand the concept of rotation and the formula for rotating a point counterclockwise.
Identify the original point and the angle of rotation correctly.
Substitute the values of ${x}$ and ${y}$ into the rotation formula correctly.
Calculate the resulting point using the formula correctly.

Frequently Asked Questions

What is the formula for rotating a point counterclockwise?
How do I determine the resulting point after rotating a point counterclockwise?
What are the common mistakes to avoid when rotating a point counterclockwise?
What are the tips and tricks for rotating a point counterclockwise?

Conclusion

In conclusion, rotating a point at ${$ (-4, 6)$}$ ${ $180^{\circ}\$}$ counterclockwise results in the point ${$ (4, -6)$}$. This transformation involves changing the position of the point while maintaining its distance from the origin. By understanding the concept of rotation and the formula for rotating a point counterclockwise, we can determine the resulting point after rotation.

Introduction

In our previous article, we explored the process of rotating a point at ${$ (-4, 6)$}$ ${ $180^{\circ}\$}$ counterclockwise and determined the resulting point. In this article, we will answer some frequently asked questions related to rotating a point counterclockwise.

Q&A

Q1: What is the formula for rotating a point counterclockwise?

A1: The formula for rotating a point counterclockwise is:

${(x', y') = (-x, -y)}$

where ${(x, y)}$ is the original point and ${(x', y')}$ is the rotated point.

Q2: How do I determine the resulting point after rotating a point counterclockwise?

A2: To determine the resulting point after rotating a point counterclockwise, you need to substitute the values of ${x}$ and ${y}$ into the rotation formula:

${(x', y') = (-x, -y)}$

Then, calculate the resulting point using the formula.

Q3: What are the common mistakes to avoid when rotating a point counterclockwise?

A3: Some common mistakes to avoid when rotating a point counterclockwise include:

Failing to understand the concept of rotation and the formula for rotating a point counterclockwise.
Not identifying the original point and the angle of rotation correctly.
Not substituting the values of ${x}$ and ${y}$ into the rotation formula correctly.
Not calculating the resulting point using the formula correctly.

Q4: What are the tips and tricks for rotating a point counterclockwise?

A4: Some tips and tricks for rotating a point counterclockwise include:

Make sure to understand the concept of rotation and the formula for rotating a point counterclockwise.
Identify the original point and the angle of rotation correctly.
Substitute the values of ${x}$ and ${y}$ into the rotation formula correctly.
Calculate the resulting point using the formula correctly.

Q5: How do I verify the answer after rotating a point counterclockwise?

A5: To verify the answer after rotating a point counterclockwise, you can check the options provided and see if the resulting point matches any of the options.

Q6: What is the resulting point after rotating a point at ${$ (-4, 6)$}$ ${ $180^{\circ}\$}$ counterclockwise?

A6: The resulting point after rotating a point at ${$ (-4, 6)$}$ ${ $180^{\circ}\$}$ counterclockwise is ${$ (4, -6)$}$.

Q7: Can I rotate a point clockwise?

A7: Yes, you can rotate a point clockwise by using the formula:

${(x', y') = (x, -y)}$

Q8: How do I rotate a point by a specific angle?

A8: To rotate a point by a specific angle, you need to use the rotation formula and substitute the values of ${x}$ , ${y}$ , and the angle of rotation into the formula.

Conclusion

In conclusion, rotating a point at ${$ (-4, 6)$}$ ${ $180^{\circ}\$}$ counterclockwise results in the point ${$ (4, -6)$}$. By understanding the concept of rotation and the formula for rotating a point counterclockwise, we can determine the resulting point after rotation. We hope this Q&A article has helped you understand the process of rotating a point counterclockwise.

Discussion

The correct answer is ${$ (4, -6)$}$. This can be verified by using the rotation formula and substituting the values of ${x}$ and ${y}$ into the formula.

Step-by-Step Solution

Understand the concept of rotation and the formula for rotating a point counterclockwise.
Identify the original point and the angle of rotation.
Substitute the values of ${x}$ and ${y}$ into the rotation formula.
Calculate the resulting point using the formula.
Verify the answer by checking the options provided.

Common Mistakes

Failing to understand the concept of rotation and the formula for rotating a point counterclockwise.
Not identifying the original point and the angle of rotation correctly.
Not substituting the values of ${x}$ and ${y}$ into the rotation formula correctly.
Not calculating the resulting point using the formula correctly.

Tips and Tricks

Make sure to understand the concept of rotation and the formula for rotating a point counterclockwise.
Identify the original point and the angle of rotation correctly.
Substitute the values of ${x}$ and ${y}$ into the rotation formula correctly.
Calculate the resulting point using the formula correctly.

Frequently Asked Questions

What is the formula for rotating a point counterclockwise?
How do I determine the resulting point after rotating a point counterclockwise?
What are the common mistakes to avoid when rotating a point counterclockwise?
What are the tips and tricks for rotating a point counterclockwise?