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The question asks for the coordinates of point \( B(-2, 4) \) after being dilated with respect to point \( P(3, -1) \) using a scale factor of \( -3 \).

### Step-by-step solution:

The formula for dilation of a point \( B(x, y) \) with respect to a center \( P(x_p, y_p) \) and a scale factor \( k \) is:

\[
B'(x', y') = \left( x_p + k(x - x_p), y_p + k(y - y_p) \right)
\]

Where:
- \( (x, y) = (-2, 4) \)
- \( (x_p, y_p) = (3, -1) \)
- Scale factor \( k = -3 \)

Let's apply the formula:

1. **For the x-coordinate**:
   \[
   x' = 3 + (-3) \times (-2 - 3) = 3 + (-3) \times (-5) = 3 + 15 = 18
   \]

2. **For the y-coordinate**:
   \[
   y' = -1 + (-3) \times (4 - (-1)) = -1 + (-3) \times (4 + 1) = -1 + (-3) \times 5 = -1 - 15 = -16
   \]

Thus, the new coordinates of point \( B \) after dilation are \( (18, -16) \).

### Correct Answer:
The correct answer is **C. \( (18, -16) \)**.

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Would you like more details or have any other questions? 

Here are 5 related questions to expand your understanding:

1. How do you find the scale factor of dilation if the original and new coordinates are given?
2. What effect does a negative scale factor have on the direction of dilation?
3. How can you verify the center of dilation given a set of points before and after dilation?
4. What is the difference between dilation and translation in coordinate geometry?
5. How can you apply dilation transformations in three-dimensional geometry?

**Tip:** Remember that a negative scale factor not only changes the size of the figure but also reflects it across the center of dilation!

Bayangan B(-2, 4) setelah didilatasikan terhadap pusat P(3, -1) dengan factor skala -3 adalah..

Find the new coordinates of point B(-2, 4) after dilation with respect to center P(3, -1) and a scale factor of -3. This problem covers key concepts of dilation and transformations in coordinate geometry.

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