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To solve this problem, we need to enlarge triangle \( ABC \) by a scale factor of \(-2\) about the origin. This involves multiplying the coordinates of each vertex of the triangle by \(-2\) to obtain the coordinates of the corresponding vertices of triangle \( A'B'C' \).

The coordinates of the vertices of triangle \( ABC \) are:

- \( A(3, 3) \)
- \( B(6, 1) \)
- \( C(0, 0) \) (the origin)

### Step 1: Apply the scale factor of \(-2\)
We multiply each coordinate by \(-2\).

1. For \( A(3, 3) \), the new coordinates \( A' \) will be:
   \[
   A' = (-2 \times 3, -2 \times 3) = (-6, -6)
   \]

2. For \( B(6, 1) \), the new coordinates \( B' \) will be:
   \[
   B' = (-2 \times 6, -2 \times 1) = (-12, -2)
   \]

3. For \( C(0, 0) \), the new coordinates \( C' \) will remain:
   \[
   C' = (0, 0) \text{ (since it's at the origin, multiplying by any scale factor doesn't change it)}
   \]

### Final Coordinates
- \( A'(-6, -6) \)
- \( B'(-12, -2) \)
- \( C'(0, 0) \)

Thus, the coordinates of \( A' \) and \( B' \) are:
- \( A'(-6, -6) \)
- \( B'(-12, -2) \)

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Would you like further details on how enlargements with negative scale factors work?

Here are five related questions to extend your understanding:
1. How do negative scale factors affect the orientation of a shape?
2. What happens if the scale factor was positive instead of negative?
3. Why does the origin remain unchanged when enlarging about the origin?
4. How do you determine the center of enlargement if it's not at the origin?
5. How can this concept of enlargement apply to real-world contexts?

**Tip**: Negative scale factors cause shapes to rotate and enlarge in the opposite direction from the center of enlargement.

Triangle ABC is being enlarged using a scale factor of -2 and the origin as the centre to give triangle A'B'C'. Work out the coordinates of A' and B'.

This problem demonstrates how to enlarge triangle ABC using a negative scale factor of -2 and the origin as the center. Learn how to calculate the new coordinates of A' and B' using transformation geometry techniques. Suitable for students in Grades 8-10.

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