To determine the rule applied to the original rectangle to create the new rectangle, we first analyze the coordinates of the original and dilated vertices.
The original rectangle has the following vertices:
- \( (12, 9) \)
- \( (12, -9) \)
- \( (-12, -9) \)
- \( (-12, 9) \)
The dilated rectangle has the following vertices:
- \( (8, 6) \)
- \( (8, -6) \)
- \( (-8, -6) \)
- \( (-8, 6) \)
Next, we will examine how each vertex of the original rectangle transforms into the new coordinate.
For the first vertex:
- From \( (12, 9) \) to \( (8, 6) \): \[ x: 12 \to 8 \quad \text{(decreased by 4)} \] \[ y: 9 \to 6 \quad \text{(decreased by 3)} \]
For the second vertex:
- From \( (12, -9) \) to \( (8, -6) \): \[ x: 12 \to 8 \quad \text{(decreased by 4)} \] \[ y: -9 \to -6 \quad \text{(decreased by 3)} \]
For the third vertex:
- From \( (-12, -9) \) to \( (-8, -6) \): \[ x: -12 \to -8 \quad \text{(increased by 4)} \] \[ y: -9 \to -6 \quad \text{(decreased by 3)} \]
For the fourth vertex:
- From \( (-12, 9) \) to \( (-8, 6) \): \[ x: -12 \to -8 \quad \text{(increased by 4)} \] \[ y: 9 \to 6 \quad \text{(decreased by 3)} \]
From this observation, we can summarize the transformations for both \( x \) and \( y \):
- For the \( x \)-coordinates, we see a shift of \(-4\) for points where \( x \) was originally positive \((12)\) and \( +4 \) where it was negative \((-12)\).
- For the \( y \)-coordinates, we see a consistent shift of \(-3\).
Thus, the transformation rule can be expressed as: \[ (x, y) \to (x-4, y-3) \]
Therefore, the correct rule applied to create the new rectangle from the original rectangle is: \[ \boxed{(x, y) \to (x - 4, y - 3)} \]