https://file.aiquickdraw.com/mathbot/file/172674668625655suc7cb.jpg

The image shows a geometric shape (a trapezoid) that is undergoing a dilation by a factor of \( \frac{1}{2} \). In dilation, every point of the figure is moved closer to or farther from a center of dilation, scaling the entire figure by a given factor. In this case, the factor is \( \frac{1}{2} \), meaning the distances between the center and the vertices of the shape will be halved.

### Step-by-Step Process for Dilation:

1. **Identify the center of dilation**: From the image, it's not clearly marked, but in common exercises like this, the origin \((0,0)\) is usually assumed as the center of dilation unless otherwise specified.

2. **Multiply the coordinates of each vertex by \( \frac{1}{2} \)**: 
   - If a point \( (x, y) \) is part of the original shape, after a dilation by a factor of \( \frac{1}{2} \), the new point will be \( \left( \frac{x}{2}, \frac{y}{2} \right) \).

   For example:
   - Vertex \( M(x_1, y_1) \) would transform to \( M'\left(\frac{x_1}{2}, \frac{y_1}{2}\right) \)
   - Similarly, apply this for vertices \( L \), \( F \), and \( W \).

3. **Plot the new points**: These scaled-down points form the dilated figure, which will look like a smaller version of the original trapezoid.

Would you like me to go through the exact coordinates of the trapezoid's vertices and calculate their transformed positions?

Here are some related questions:
1. How do you identify the center of dilation when it's not given explicitly?
2. What happens if the dilation factor is greater than 1?
3. What is the impact of a negative dilation factor on a geometric figure?
4. How can you verify if a dilation transformation has been performed correctly?
5. Can you describe the differences between dilation and translation?

**Tip:** When performing dilation, always double-check that you are applying the dilation factor to all points uniformly for an accurate transformation.

What is the dilation of a shape by a factor of 1/2?

Explore the concept of dilation in geometry by learning how a trapezoid dilates by a factor of 1/2. This guide includes a step-by-step demonstration on calculating new vertex coordinates and understanding the transformations on the coordinate plane. Suitable for students in Grades 7-9.

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