A trapezoid was transformed on a coordinate grid using the rule (x, y) 
 (-x, y). Which of the following describes this transformation?
Responses


The rule \((x, y) \to (-x, y)\) describes a **reflection over the y-axis**. 

Explanation:
- This transformation changes the sign of the x-coordinate while leaving the y-coordinate unchanged.
- Geometrically, this means that every point on the figure is "flipped" across the y-axis, so the distances to the y-axis are preserved but the points switch sides.

Would you like more details or have any other questions?

Here are five related questions:
1. What happens to a figure if you apply the transformation \((x, y) \to (x, -y)\)?
2. How would you describe a rotation of 90° counterclockwise about the origin in coordinate terms?
3. What is the effect of reflecting a figure over both the x- and y-axes?
4. Can a trapezoid still be congruent to itself after multiple reflections? Why or why not?
5. How can you determine if a transformation is an isometry (distance-preserving)?

**Tip**: Reflections preserve the size and shape of a figure, making them isometries!

A trapezoid was transformed on a coordinate grid using the rule (x, y) → (-x, y). Which of the following describes this transformation?

Explore how a trapezoid is transformed using the rule (x, y) → (-x, y), which describes a reflection over the y-axis. Learn key concepts in coordinate geometry and geometric transformations, ideal for students in Grades 8-10.

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