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The problem provided involves a square \( BCDE \) with vertices \( B(-3, -4) \), \( C(0, -3) \), \( D(1, -6) \), and \( E(-2, -7) \). The task is to apply a dilation to the square using a scale factor of \( k = 4 \), with the center of dilation at \( (0, -5) \).

### Steps to Solve the Dilation:

1. **Dilation Formula:**
   The dilation formula for any point \( (x, y) \) with respect to a center of dilation \( (x_c, y_c) \) and scale factor \( k \) is:
   \[
   (x', y') = (x_c + k(x - x_c), y_c + k(y - y_c))
   \]
   where \( (x', y') \) are the new coordinates after dilation.

2. **Center of Dilation:** \( (0, -5) \)
   We'll apply this formula for each vertex of the square.

3. **Dilation for each vertex:**

   - For \( B(-3, -4) \):
     \[
     x' = 0 + 4(-3 - 0) = -12, \quad y' = -5 + 4(-4 - (-5)) = -5 + 4(1) = -1
     \]
     So, the new coordinates of \( B' \) are \( (-12, -1) \).

   - For \( C(0, -3) \):
     \[
     x' = 0 + 4(0 - 0) = 0, \quad y' = -5 + 4(-3 - (-5)) = -5 + 4(2) = 3
     \]
     So, the new coordinates of \( C' \) are \( (0, 3) \).

   - For \( D(1, -6) \):
     \[
     x' = 0 + 4(1 - 0) = 4, \quad y' = -5 + 4(-6 - (-5)) = -5 + 4(-1) = -9
     \]
     So, the new coordinates of \( D' \) are \( (4, -9) \).

   - For \( E(-2, -7) \):
     \[
     x' = 0 + 4(-2 - 0) = -8, \quad y' = -5 + 4(-7 - (-5)) = -5 + 4(-2) = -13
     \]
     So, the new coordinates of \( E' \) are \( (-8, -13) \).

### New Coordinates after Dilation:
- \( B'(-12, -1) \)
- \( C'(0, 3) \)
- \( D'(4, -9) \)
- \( E'(-8, -13) \)

These are the vertices of the square after applying the dilation.

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Would you like any further details or clarifications?

### Additional Questions:
1. How do you find the center of dilation if not given directly?
2. What happens to the shape of the figure when you apply a dilation with a scale factor less than 1?
3. Can dilation change the orientation of a figure? Why or why not?
4. What is the effect of a negative scale factor in dilation?
5. How would you apply dilation if the center is outside the coordinate plane?

**Tip:** Always double-check your calculations, especially when applying a scale factor, as small errors can significantly change the shape or size.

Apply a dilation to square BCDE with vertices B(-3, -4), C(0, -3), D(1, -6), and E(-2, -7). Use a scale factor of k=4 and a center of dilation at (0, -5).

Learn how to apply a dilation transformation to square BCDE with vertices B(-3, -4), C(0, -3), D(1, -6), and E(-2, -7). The dilation uses a scale factor of 4 with the center of dilation at (0, -5). The solution includes key formulas and concepts from geometry, suitable for students in Grades 8-10.

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