Solve problems involving reflection

Oct 13, 2025 by talynt.org 130 views

Understanding Reflection Across the Y-axis

When a point is reflected across the y-axis, the x-coordinate changes sign, while the y-coordinate remains the same. This is because the y-axis acts as a mirror, and the reflection of a point across the y-axis is obtained by changing the sign of its x-coordinate.

Reflection Across the Y-axis: A Step-by-Step Explanation

To reflect a point across the y-axis, follow these steps:

Identify the x-coordinate: The x-coordinate of the point is the value that will change sign after reflection.
Change the sign of the x-coordinate: Multiply the x-coordinate by -1 to change its sign.
Keep the y-coordinate the same: The y-coordinate remains unchanged after reflection across the y-axis.

Applying Reflection to Point Z(-3.9, -9.3)

Now, let's apply the reflection process to point Z(-3.9, -9.3):

Identify the x-coordinate: The x-coordinate of point Z is -3.9.
Change the sign of the x-coordinate: Multiply -3.9 by -1 to get 3.9.
Keep the y-coordinate the same: The y-coordinate of point Z is -9.3, which remains unchanged after reflection.

The Coordinates of Point Z after Reflection

After reflecting point Z across the y-axis, the new coordinates are:

x-coordinate: 3.9
y-coordinate: -9.3

Therefore, the coordinates of point Z after reflection across the y-axis are (3.9, -9.3).

Conclusion

Frequently Asked Questions

What happens to the x-coordinate after reflection across the y-axis? The x-coordinate changes sign after reflection across the y-axis.
What happens to the y-coordinate after reflection across the y-axis? The y-coordinate remains unchanged after reflection across the y-axis.
How do I reflect a point across the y-axis? To reflect a point across the y-axis, change the sign of its x-coordinate and keep the y-coordinate the same.

Example Problems

Reflect the point (2.5, 4.2) across the y-axis.
Reflect the point (-1.8, 6.5) across the y-axis.
Reflect the point (0.9, -2.1) across the y-axis.

Practice Problems

Reflect the point (3.6, -8.9) across the y-axis.
Reflect the point (-4.2, 2.1) across the y-axis.
Reflect the point (1.5, -6.8) across the y-axis.

Real-World Applications

Reflection across the y-axis has numerous real-world applications, including:

Geometry and Trigonometry: Reflection across the y-axis is used to solve problems involving geometric shapes and trigonometric functions.
Physics and Engineering: Reflection across the y-axis is used to model real-world phenomena, such as the motion of objects and the behavior of electrical circuits.
Computer Graphics: Reflection across the y-axis is used to create 2D and 3D graphics, including animations and special effects.

Conclusion

In conclusion, reflecting a point across the y-axis involves changing the sign of its x-coordinate while keeping the y-coordinate the same. By applying this process to point Z(-3.9, -9.3), we obtained the new coordinates (3.9, -9.3). Reflection across the y-axis has numerous real-world applications, including geometry, trigonometry, physics, engineering, and computer graphics.

Q&A: Reflection Across the Y-axis

Q: What is reflection across the y-axis?

A: Reflection across the y-axis is a process where a point is reflected across the y-axis, resulting in a change in the sign of its x-coordinate while keeping the y-coordinate the same.

Q: How do I reflect a point across the y-axis?

A: To reflect a point across the y-axis, follow these steps:

Identify the x-coordinate: The x-coordinate of the point is the value that will change sign after reflection.
Change the sign of the x-coordinate: Multiply the x-coordinate by -1 to change its sign.
Keep the y-coordinate the same: The y-coordinate remains unchanged after reflection across the y-axis.

Q: What happens to the x-coordinate after reflection across the y-axis?

A: The x-coordinate changes sign after reflection across the y-axis.

Q: What happens to the y-coordinate after reflection across the y-axis?

A: The y-coordinate remains unchanged after reflection across the y-axis.

Q: How do I apply reflection to a point with negative x-coordinate?

A: To apply reflection to a point with negative x-coordinate, follow these steps:

Identify the x-coordinate: The x-coordinate of the point is the value that will change sign after reflection.
Change the sign of the x-coordinate: Multiply the x-coordinate by -1 to change its sign.
Keep the y-coordinate the same: The y-coordinate remains unchanged after reflection across the y-axis.

Q: How do I apply reflection to a point with positive x-coordinate?

A: To apply reflection to a point with positive x-coordinate, follow these steps:

Identify the x-coordinate: The x-coordinate of the point is the value that will change sign after reflection.
Change the sign of the x-coordinate: Multiply the x-coordinate by -1 to change its sign.
Keep the y-coordinate the same: The y-coordinate remains unchanged after reflection across the y-axis.

Q: What is the difference between reflection across the x-axis and reflection across the y-axis?

A: Reflection across the x-axis involves changing the sign of the y-coordinate, while reflection across the y-axis involves changing the sign of the x-coordinate.

Q: How do I reflect a point across the x-axis?

A: To reflect a point across the x-axis, follow these steps:

Identify the y-coordinate: The y-coordinate of the point is the value that will change sign after reflection.
Change the sign of the y-coordinate: Multiply the y-coordinate by -1 to change its sign.
Keep the x-coordinate the same: The x-coordinate remains unchanged after reflection across the x-axis.

Q: What are some real-world applications of reflection across the y-axis?

A: Reflection across the y-axis has numerous real-world applications, including:

Geometry and Trigonometry: Reflection across the y-axis is used to solve problems involving geometric shapes and trigonometric functions.
Physics and Engineering: Reflection across the y-axis is used to model real-world phenomena, such as the motion of objects and the behavior of electrical circuits.
Computer Graphics: Reflection across the y-axis is used to create 2D and 3D graphics, including animations and special effects.

Q: How do I practice reflection across the y-axis?

A: To practice reflection across the y-axis, try the following:

Reflect points across the y-axis: Practice reflecting points across the y-axis using different coordinates.
Solve problems involving reflection: Practice solving problems that involve reflection across the y-axis.
Use online resources: Use online resources, such as calculators and graphing tools, to practice reflection across the y-axis.

Conclusion

In conclusion, reflection across the y-axis is a fundamental concept in mathematics that involves changing the sign of a point's x-coordinate while keeping the y-coordinate the same. By understanding how to reflect points across the y-axis, you can solve problems involving geometric shapes, trigonometric functions, and real-world phenomena.