https://file.aiquickdraw.com/mathbot/file/1734616566088uveu2ey3.jpg

Let's solve the given problem.

### Problem Details:
- Original vertex \( A \) is located at \( (6, 4) \).
- Triangle \( ABC \) is dilated with a **scale factor** of \( 0.5 \), with the center of dilation at the origin \( (0, 0) \).
- The question asks for the new coordinates of \( A' \) after dilation.

### Solution:
1. The formula for dilation when the center is at the origin is:
   \[
   A'(x', y') = (k \cdot x, k \cdot y)
   \]
   where:
   - \( (x, y) \) are the original coordinates,
   - \( k \) is the scale factor.

2. Substitute the given values:
   - \( k = 0.5 \),
   - \( (x, y) = (6, 4) \).

   Perform the calculations:
   \[
   x' = 0.5 \cdot 6 = 3, \quad y' = 0.5 \cdot 4 = 2.
   \]

3. The new coordinates of \( A' \) are \( (3, 2) \).

### Final Answer:
The coordinates of vertex \( A' \) are **(3, 2)**, which corresponds to **option A**.

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Would you like a detailed explanation of the dilation concept? Let me know! Here are some related questions for practice:

1. How do you calculate the coordinates of a point after a dilation with a scale factor greater than 1?
2. What happens to the shape of a figure when the scale factor is less than 1?
3. How do you determine the center of dilation if it is not the origin?
4. How is the area of a figure affected by a dilation?
5. Can a dilation ever change the orientation of a shape?

### Tip:
Always multiply each coordinate by the scale factor to ensure the dilation transformation is applied correctly.

On a coordinate plane, vertex A for triangle ABC is located at (6, 4). Triangle ABC is dilated by a scale factor of 0.5 with the center of dilation at the origin. The resulting image is triangle A'B'C'. What are the coordinates of vertex A'?

Learn how to find the coordinates of a point after dilation. In this problem, triangle ABC is dilated with a scale factor of 0.5, centered at the origin. Determine the coordinates of vertex A'. Suitable for Grades 8-10.

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