https://file.aiquickdraw.com/mathbot/file/1727283853015gy1obkla.jpg

The problem involves a geometric transformation called **dilation**. Figure \( ABCDE \) is being dilated by a scale factor of **3**, with the origin \((0,0)\) as the center of dilation, to produce the image \( A'B'C'D'E' \).

### Key Concepts:
- **Dilation**: When a figure is enlarged or reduced from a point (the center of dilation), with a scale factor determining how much larger or smaller the figure becomes.
- **Scale Factor**: In this case, it is 3, meaning the distance of each point from the origin will triple.
- **Center of Dilation**: The origin \((0, 0)\).

### Coordinates of Points:
We need to find the coordinates of point \( B' \), which is the transformed version of point \( B \). 

1. **Coordinate of Point \( B \)**:
   - From the graph, the coordinates of point \( B \) are \( (3, 4) \).

2. **Dilation Calculation**:
   - Since the scale factor is **3**, multiply both coordinates of point \( B \) by **3**.
   - Coordinates of \( B' \): 
     \[
     B'(3 \times 3, 4 \times 3) = B'(9, 12)
     \]

Thus, the ordered pair for the coordinate of \( B' \) is \( (9, 12) \).

Would you like more details or clarification on the dilation process?

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### Further Questions:
1. What would be the coordinates of \( C' \) after the dilation?
2. How does a dilation affect the angles of a figure?
3. What would happen to the figure if the scale factor was less than 1?
4. How do you determine the center of dilation from a transformation?
5. Can dilation be considered a rigid transformation? Why or why not?

### Tip:
When performing a dilation, always multiply both the x- and y-coordinates of each point by the scale factor, keeping the center of dilation constant.

Figure ABCDE is transformed into Figure A'B'C'D'E' through a dilation, using the origin as the center and a scale factor of 3. What is the coordinate of B'?

Explore the dilation transformation of figure ABCDE with a scale factor of 3, using the origin as the center of dilation. This geometry problem focuses on how to determine the coordinates of B' after dilation. Suitable for Grade 8 students.

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