https://file.aiquickdraw.com/mathbot/file/1727212365695nx8y7tqp.jpg

To reflect quadrilateral ABCD over the y-axis, we apply the following rule for each vertex: 

- When reflecting over the y-axis, the \(x\)-coordinate of each point changes sign, while the \(y\)-coordinate stays the same.

The coordinates of the vertices \(A\), \(B\), \(C\), and \(D\) are needed from the graph. I'll analyze the positions of the points from the image:

1. **Coordinates of A**: \( (0, 0) \)
   - After reflection over the y-axis: \( A' = (0, 0) \) (no change since it's on the y-axis).

2. **Coordinates of B**: \( (-1, -2) \)
   - After reflection over the y-axis: \( B' = (1, -2) \).

3. **Coordinates of C**: \( (-3, -1) \)
   - After reflection over the y-axis: \( C' = (3, -1) \).

4. **Coordinates of D**: \( (-2, 1) \)
   - After reflection over the y-axis: \( D' = (2, 1) \).

These new points represent the reflection of quadrilateral ABCD over the y-axis. Let me know if you need a further breakdown!

Here are five related questions:

1. How would you reflect a shape over the x-axis instead of the y-axis?
2. What happens to the coordinates when reflecting over the origin?
3. How do you calculate the distance between two points after reflection?
4. What is the general transformation rule for reflecting over any vertical line \(x = k\)?
5. How can you verify the reflected image using a distance formula?

**Tip:** When reflecting a point, always check the axis of reflection carefully, as only one coordinate changes depending on the axis.

Learn how to reflect quadrilateral ABCD over the y-axis using the transformation rule. This math problem involves understanding reflections in coordinate geometry, where the x-coordinate changes its sign while the y-coordinate remains the same. Perfect for students in Grades 6-8.

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