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The problem involves a point on a triangle being transformed through a dilation and then a reflection.

### Given:
- The original point is \( (2, 1) \).
- The dilation has a scale factor of 2.5, centered at the origin.
- After the dilation, the figure is reflected about the y-axis.

### Steps to solve:

1. **Dilation**: 
   A dilation with a scale factor \( k \) and center at the origin means multiplying both coordinates of the point by \( k \).
   \[
   (x', y') = (2 \times 2.5, 1 \times 2.5) = (5, 2.5)
   \]

2. **Reflection**: 
   Reflecting a point across the y-axis changes the sign of the x-coordinate. So, the new point will be:
   \[
   (-x', y') = (-5, 2.5)
   \]

Thus, the new x-coordinate after both transformations is \( \boxed{-5} \).

Would you like further clarification or details on this process? 

Here are five related questions:
1. What happens when a triangle is reflected across the x-axis instead?
2. How does the scale factor affect the size of geometric shapes during dilation?
3. What is the effect of rotating a point instead of reflecting it?
4. How would you find the coordinates of the other vertices of the triangle after dilation and reflection?
5. Can the reflection be performed before dilation, and how would that change the result?

**Tip**: Always apply dilations before reflections when performing multiple transformations, unless instructed otherwise.

The point (2, 1) is 1 of the 3 vertices of a triangle. The triangle is dilated by a scale factor of 2.5 with center of dilation about the origin, then reflected about the y-axis. What is the new x-coordinate of the corresponding vertex?

This geometry problem involves dilating a triangle's vertex by a scale factor of 2.5 and reflecting it across the y-axis. Learn how to apply coordinate transformations to find the new x-coordinate of the vertex. Suitable for Grade 8 students.

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