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To solve this problem, we need to find the new coordinates of vertices \( A' \) and \( B' \) after enlarging the shape by a scale factor of \( -2 \), using the point \( (2, 4) \) as the center of enlargement.

### Step-by-Step Solution:

1. **Identify the original coordinates**:
   - The original coordinates of point \( A \) (from the grid) are approximately \( (5, 6) \).
   - The original coordinates of point \( B \) are approximately \( (10, 4) \).
   
2. **Apply the formula for enlargement**:
   When enlarging with a scale factor \( k \) from a center \( (x_c, y_c) \), the formula for the new coordinates of a point \( (x, y) \) is:
   \[
   (x', y') = \left( x_c + k(x - x_c), y_c + k(y - y_c) \right)
   \]
   Here, \( k = -2 \), and the center is \( (2, 4) \).

3. **Find the new coordinates for \( A' \)**:
   - Original \( A = (5, 6) \).
   - Apply the formula:
     \[
     x' = 2 + (-2)(5 - 2) = 2 + (-2)(3) = 2 - 6 = -4
     \]
     \[
     y' = 4 + (-2)(6 - 4) = 4 + (-2)(2) = 4 - 4 = 0
     \]
   - Thus, \( A' = (-4, 0) \).

4. **Find the new coordinates for \( B' \)**:
   - Original \( B = (10, 4) \).
   - Apply the formula:
     \[
     x' = 2 + (-2)(10 - 2) = 2 + (-2)(8) = 2 - 16 = -14
     \]
     \[
     y' = 4 + (-2)(4 - 4) = 4 + (-2)(0) = 4
     \]
   - Thus, \( B' = (-14, 4) \).

### Final Coordinates:
- \( A' = (-4, 0) \)
- \( B' = (-14, 4) \)

Would you like further details or have any questions?

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Here are 5 questions that expand on this problem:
1. What happens to the orientation of the shape when the scale factor is negative?
2. How would the coordinates change if the scale factor were positive instead of negative?
3. What are the properties of shapes under enlargement by a negative scale factor?
4. How can we verify the accuracy of the new coordinates after transformation?
5. How does the distance between the points and the center of enlargement change with a scale factor?

**Tip**: When the scale factor is negative, the shape not only enlarges or shrinks but also reflects through the center of enlargement.

This shape is being enlarged by a scale factor of -2, using (2,4) as the centre. Work out the coordinates of vertices A' and B'.

Learn how to enlarge a shape using a scale factor of -2, with the center of enlargement at (2,4). Find the new coordinates of points A' and B' through the transformation formula. Suitable for students in Grades 8-10, covering coordinate geometry and transformations.

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