
A trapezoid was transformed on a coordinate grid using the rule (x, y) → (–x, y). Which of the following describes this transformation?
A. A reflection across the y-axis
B. A 180° clockwise rotation about the origin
C. A 90° clockwise rotation about the origin
D. A reflection across the x-axis


The transformation rule given is \((x, y) \rightarrow (-x, y)\), which means that the \(x\)-coordinate changes sign, while the \(y\)-coordinate remains the same.

This transformation reflects all points across the **y-axis**, because when reflecting across the y-axis, the \(x\)-coordinate of any point changes its sign while the \(y\)-coordinate remains unchanged.

Thus, the correct answer is:

**A. A reflection across the y-axis**

Would you like more details on how to identify different transformations or have any questions?

Here are 5 related questions to expand on this concept:
1. How would the transformation \((x, y) \rightarrow (x, -y)\) affect a figure on the coordinate plane?
2. What is the result of applying the transformation \((x, y) \rightarrow (-x, -y)\)?
3. How does a 90° clockwise rotation about the origin transform the coordinates of a point?
4. Can you describe how a figure would change after a 180° clockwise rotation about the origin?
5. What are the general rules for reflecting a point across both the x-axis and y-axis?

**Tip:** Always check how transformations affect the \(x\)- and \(y\)-coordinates to quickly identify the type of transformation.

A trapezoid was transformed on a coordinate grid using the rule (x, y) → (–x, y). Which of the following describes this transformation? A. A reflection across the y-axis B. A 180° clockwise rotation about the origin C. A 90° clockwise rotation about the origin D. A reflection across the x-axis

Understand the transformation rule (x, y) → (–x, y) and how it reflects points across the y-axis. This problem explores key concepts in coordinate geometry and transformations, suitable for students in Grades 8-10.

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