Calculating the Reflected Point

Oct 13, 2025 by miodeya.com 29 views

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.