What Is The Ordered Pair That Represents The Point $(-3,8)$ After A Reflection Over The $ X X X − A X I S -axis − A X I S ?A. $(-8,-3)$B. $(8,-3)$C. $ ( − 3 , − 8 ) (-3,-8) ( − 3 , − 8 ) [/tex]D. $(3,8)$

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Understanding Reflection Over the $x$-axis

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

Reflection of the Point $(-3,8)$ Over the $x$-axis

To find the ordered pair that represents the point $(-3,8)$ after a reflection over the $x$-axis, we need to change the sign of its $y$-coordinate. The $x$-coordinate remains the same.

Calculating the Reflected Point

The original point is $(-3,8)$. To reflect this point over the $x$-axis, we change the sign of its $y$-coordinate. Therefore, the reflected point is $(-3,-8)$.

Conclusion

The ordered pair that represents the point $(-3,8)$ after a reflection over the $x$-axis is $(-3,-8)$. This is because the reflection of a point over the $x$-axis is obtained by changing the sign of its $y$-coordinate, while the $x$-coordinate remains the same.

Understanding the Options

Let's analyze the options given:

A. $(-8,-3)$ B. $(8,-3)$ C. $(-3,-8)$ D. $(3,8)$

Eliminating Incorrect Options

Option A, $(-8,-3)$, is incorrect because the $x$-coordinate has changed, but the $y$-coordinate has not been changed in sign. Option B, $(8,-3)$, is also incorrect because the $x$-coordinate has changed, and the $y$-coordinate has not been changed in sign. Option D, $(3,8)$, is incorrect because the $x$-coordinate has changed, and the $y$-coordinate has not been changed in sign.

Conclusion

The correct option is C, $(-3,-8)$. This is because the reflection of the point $(-3,8)$ over the $x$-axis is obtained by changing the sign of its $y$-coordinate, while the $x$-coordinate remains the same.

Reflection Over the $x$-axis: Key Concepts

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

Real-World Applications of Reflection Over the $x$-axis

  • Reflection over the $x$-axis is used in various real-world applications, such as:
    • Mirrors and reflection in art and design
    • Physics and engineering, where reflection is used to analyze and solve problems
    • Computer graphics and animation, where reflection is used to create realistic images and animations

Conclusion

In conclusion, the ordered pair that represents the point $(-3,8)$ after a reflection over the $x$-axis is $(-3,-8)$. This is because the reflection of a point over the $x$-axis is obtained by changing the sign of its $y$-coordinate, while the $x$-coordinate remains the same.

Frequently Asked Questions

Q1: What is reflection over the $x$-axis?

A1: Reflection over the $x$-axis is a transformation that changes the sign of a point's $y$-coordinate, while keeping the $x$-coordinate the same.

Q2: How do I reflect a point over the $x$-axis?

A2: To reflect a point over the $x$-axis, you need to change the sign of its $y$-coordinate. For example, if the point is $(x, y)$, the reflected point will be $(x, -y)$.

Q3: What happens to the $x$-coordinate when a point is reflected over the $x$-axis?

A3: The $x$-coordinate remains the same when a point is reflected over the $x$-axis. Only the $y$-coordinate changes sign.

Q4: Can I reflect a point over the $x$-axis using a mirror?

A4: Yes, you can reflect a point over the $x$-axis using a mirror. The mirror acts as the $x$-axis, and the reflection of the point is obtained by changing the sign of its $y$-coordinate.

Q5: How do I apply reflection over the $x$-axis in real-world situations?

A5: Reflection over the $x$-axis is used in various real-world applications, such as:

  • Mirrors and reflection in art and design
  • Physics and engineering, where reflection is used to analyze and solve problems
  • Computer graphics and animation, where reflection is used to create realistic images and animations

Q6: Can I reflect a point over the $x$-axis using a coordinate plane?

A6: Yes, you can reflect a point over the $x$-axis using a coordinate plane. The $x$-axis acts as a mirror, and the reflection of the point is obtained by changing the sign of its $y$-coordinate.

Q7: What is the difference between reflection over the $x$-axis and reflection over the $y$-axis?

A7: The main difference between reflection over the $x$-axis and reflection over the $y$-axis is that reflection over the $x$-axis changes the sign of the $y$-coordinate, while reflection over the $y$-axis changes the sign of the $x$-coordinate.

Q8: Can I reflect a point over the $x$-axis using a formula?

A8: Yes, you can reflect a point over the $x$-axis using a formula. The formula for reflecting a point $(x, y)$ over the $x$-axis is $(x, -y)$.

Q9: How do I determine if a point is reflected over the $x$-axis?

A9: To determine if a point is reflected over the $x$-axis, you need to check if the $y$-coordinate has changed sign. If the $y$-coordinate has changed sign, then the point is reflected over the $x$-axis.

Q10: Can I reflect a point over the $x$-axis using a graphing calculator?

A10: Yes, you can reflect a point over the $x$-axis using a graphing calculator. The graphing calculator can be used to graph the point and its reflection over the $x$-axis.

Conclusion

In conclusion, reflection over the $x$-axis is a transformation that changes the sign of a point's $y$-coordinate, while keeping the $x$-coordinate the same. This transformation is used in various real-world applications, such as mirrors and reflection in art and design, physics and engineering, and computer graphics and animation.