
Apply the rule 
f(x,y)=(x,−y)
Connect the corresponding preimage and image points.  These segments are ______.

parellel, congruent, or perpundicular

Given the rule \( f(x, y) = (x, -y) \), the transformation reflects points across the **x-axis**. 

To analyze the relationship between the segments connecting corresponding preimage and image points:

1. Consider any point \( P(x, y) \). Its image under the transformation is \( P'(x, -y) \), where the y-coordinate is negated while the x-coordinate remains the same.
2. The segment connecting \( P \) and \( P' \) will be vertical, as their x-coordinates are the same but their y-coordinates are opposite.

Therefore, all such segments are **perpendicular** to the x-axis, which means they are **perpendicular** to the axis of reflection. 

The correct answer is: **perpendicular**.

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Would you like a more detailed explanation, or do you have any questions? 

Here are five related questions you might find interesting:

1. What happens if the reflection is across the y-axis instead?
2. How would the transformation change if it were \( f(x, y) = (-x, y) \)?
3. What is the geometric interpretation of \( f(x, y) = (-x, -y) \)?
4. Can a reflection transformation change the length of a line segment?
5. How does this transformation affect the orientation of a shape?

**Tip**: Reflections maintain distance between points but reverse orientation.

Apply the rule f(x,y)=(x,−y). Connect the corresponding preimage and image points. These segments are parallel, congruent, or perpendicular?

Explore how the transformation f(x, y) = (x, -y) reflects points across the x-axis. Understand why the segments connecting corresponding preimage and image points are perpendicular to the axis of reflection. This solution covers reflection and coordinate geometry concepts suitable for Grades 8-10.

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