https://file.aiquickdraw.com/mathbot/file/17261782482651fa83r4d.jpg

Plot the image of quadrilateral
\[ABCD\] under a reflection across the
\[x\]-axis.

To reflect the quadrilateral \( ABCD \) across the \( x \)-axis, you will need to change the sign of the \( y \)-coordinates of each vertex while keeping the \( x \)-coordinates unchanged. Let's apply this transformation to each point:

- **Point A**: Currently at \( (-3, 2) \). Reflecting across the \( x \)-axis changes this to \( (-3, -2) \).
- **Point B**: Currently at \( (3, 2) \). Reflecting across the \( x \)-axis changes this to \( (3, -2) \).
- **Point C**: Currently at \( (2, -4) \). Reflecting across the \( x \)-axis changes this to \( (2, 4) \).
- **Point D**: Currently at \( (-4, 2) \). Reflecting across the \( x \)-axis changes this to \( (-4, -2) \).

The new points after reflection are:

- \( A' = (-3, -2) \)
- \( B' = (3, -2) \)
- \( C' = (2, 4) \)
- \( D' = (-4, -2) \)

You can now plot these points to form the reflected image of quadrilateral \( ABCD \). Would you like further details or clarifications?

Here are some related questions to explore:

1. How does reflecting over the \( y \)-axis differ from reflecting over the \( x \)-axis?
2. What other transformations could be applied to this quadrilateral besides reflection?
3. How do reflections affect the area and perimeter of a shape?
4. What happens to the angles of a shape when it is reflected across the \( x \)-axis?
5. Can you reflect a shape across both the \( x \)-axis and \( y \)-axis simultaneously?

**Tip:** When reflecting a point, always consider the axis you're reflecting over and only change the coordinate related to that axis.

Plot the image of quadrilateral ABCD under a reflection across the x-axis.

Learn how to reflect quadrilateral ABCD across the x-axis by changing the signs of the y-coordinates of each vertex. This problem involves key concepts from coordinate geometry and is suitable for students in Grades 6-8.

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