https://file.aiquickdraw.com/mathbot/file/1726616098858w3h9v0ei.jpg

The image shows a coordinate plane with a polygon plotted on it. The task is to reduce the side lengths of this polygon by half using the coordinate plane. Here's how you can do that:

### Step-by-Step Instructions:
1. **Identify the Coordinates of the Vertices**: First, determine the exact coordinates of the polygon's vertices. Let's assume the vertices are at points \((x_1, y_1), (x_2, y_2), (x_3, y_3), (x_4, y_4)\).
2. **Halve the Distances from the Origin**: To reduce the side lengths of the polygon by half, we need to scale each of the vertex coordinates by \( \frac{1}{2} \). For any vertex at \((x, y)\), the new vertex will be at \(\left( \frac{x}{2}, \frac{y}{2} \right)\).
3. **Plot the New Polygon**: After halving the coordinates, plot the new polygon on the coordinate plane. Each vertex will now be closer to the origin, and the polygon will have the same shape but with sides that are half as long.

Would you like me to help you identify the exact coordinates of the vertices from the image and calculate the new, reduced coordinates?

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### Related Questions:
1. How can you generalize the method to scale a figure by a factor other than \( \frac{1}{2} \)?
2. What happens to the area of the polygon when the side lengths are reduced by half?
3. How can you determine the center of a polygon in a coordinate plane?
4. How would you rotate this polygon by 90 degrees around the origin?
5. What transformations are needed to reflect this polygon across the x-axis?

### Tip:
When scaling a shape on a coordinate plane, always multiply both the x and y coordinates of each vertex by the scaling factor!

Use the coordinate plane to reduce the side lengths of the figure below by half. Use the Polygon Tool to plot the image.

Learn how to reduce the side lengths of a polygon by half using a coordinate plane. This math problem involves key concepts like geometric scaling, using the formula (x, y) → (kx, ky) where k = 1/2. Suitable for students in Grades 7-9.

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