Cai uaes a computer program to resize photos for the online school newspaper. Rectangle DEFG represents the photo. She drags the top right corner of the rectangle along the dashed line to form the image rectangle D'E'F'G'. What are the coordinates of the vertices of image rectangle D'E'F'G'?

To determine the coordinates of the vertices of the image rectangle \( D'E'F'G' \), we need to have the initial coordinates of the rectangle \( DEFG \) and the transformation applied (such as resizing or translation). Since you mentioned that Cai drags the top right corner, this suggests a resizing operation.

In this case, you would follow these steps:

1. **Identify Initial Coordinates of Rectangle \( DEFG \)**: Suppose the initial coordinates of the vertices of the rectangle \( DEFG \) are given as:

   \[
   D(x_1, y_1), E(x_2, y_2), F(x_3, y_3), G(x_4, y_4)
   \]

2. **Determine the Transformation**: You mentioned Cai drags the top right corner (which would be \( G \) if \( G \) is the top right corner) along a dashed line. This transformation could be a scaling or stretching of the rectangle, either horizontally, vertically, or both.

3. **New Coordinates**: If the transformation affects only the top right corner, the coordinates of the other vertices might remain the same, and only the top right corner would change. Let's assume that the new coordinates of the top right corner (previously \( G \)) become \( G'(x_4', y_4') \).

   The new vertices of the image rectangle \( D'E'F'G' \) will be:
   - \( D'(x_1, y_1) \) (same as \( D \))
   - \( E'(x_2, y_2) \) (same as \( E \))
   - \( F'(x_3, y_3) \) (same as \( F \))
   - \( G'(x_4', y_4') \) (new coordinates for the top right corner)

To provide a precise answer, please provide either the original coordinates of \( DEFG \) or the exact nature of the transformation (such as scaling factor or direction).

Would you like more details on how resizing operations affect coordinates? Here are five related questions:

1. How do scaling factors affect the coordinates of a rectangle?
2. How can we calculate the area of the image rectangle after resizing?
3. What are the properties of similar rectangles in geometry?
4. How do translations and resizing differ in coordinate changes?
5. How would the resizing process differ if the dragging was in the vertical direction only?

**Tip**: Always pay attention to whether a transformation changes all vertices or only specific ones like the top corner.

Cai uses a computer program to resize photos for the online school newspaper. Rectangle DEFG represents the photo. She drags the top right corner of the rectangle along the dashed line to form the image rectangle D'E'F'G'. What are the coordinates of the vertices of image rectangle D'E'F'G'?

Learn how to calculate the new coordinates of the vertices of a rectangle after a resizing transformation. The problem involves dragging the top right corner of rectangle DEFG to form a new image rectangle D'E'F'G'. This solution covers concepts in coordinate geometry, transformations, and scaling. Suitable for students in Grades 8-10.

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