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Grafica la imagen del cuadrilátero ABCD  al aplicar una reflexión a través del eje x

To graph the reflection of the quadrilateral \( ABCD \) across the \( x \)-axis, we need to reflect each vertex of the quadrilateral over the \( x \)-axis. When reflecting a point across the \( x \)-axis, the \( x \)-coordinate remains the same, while the \( y \)-coordinate changes sign.

Let's determine the new coordinates for each vertex after reflection:

### Step 1: Identify the Coordinates of Each Vertex
From the image, the approximate coordinates of the vertices are:

- \( A(1, 2) \)
- \( B(3, 1) \)
- \( C(2, -5) \)
- \( D(-1, -2) \)

### Step 2: Reflect Each Point Across the \( x \)-axis
To reflect across the \( x \)-axis, we keep the \( x \)-coordinate the same and multiply the \( y \)-coordinate by -1.

- \( A' = (1, -2) \)
- \( B' = (3, -1) \)
- \( C' = (2, 5) \)
- \( D' = (-1, 2) \)

### Step 3: Plot the Reflected Quadrilateral
Now, plot the points \( A' \), \( B' \), \( C' \), and \( D' \) on the same grid and connect them to form the reflected quadrilateral \( A'B'C'D' \).

Would you like a visualization of this reflected quadrilateral or any further details on the reflection process? 

### 5 Related Questions:
1. How do you perform a reflection across the \( y \)-axis?
2. What is the general rule for reflecting a point across the line \( y = x \)?
3. How can reflections be used to determine symmetry in geometric shapes?
4. How do you find the coordinates of a point after rotating it 90 degrees about the origin?
5. What transformations would result in the quadrilateral \( ABCD \) being congruent to its reflection?

### Tip:
When reflecting a shape, remember to check if any two points on the shape are equidistant from the axis of reflection to ensure accuracy.

Grafica la imagen del cuadrilátero ABCD al aplicar una reflexión a través del eje x.

Learn how to reflect the quadrilateral ABCD across the x-axis by determining new coordinates for each vertex and plotting the reflected shape on the coordinate plane. This problem demonstrates key geometry concepts related to reflections and transformations, suitable for students in Grades 7-9.

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