https://file.aiquickdraw.com/mathbot/file/1726231466001lu7thgrv.jpg

To solve this question, we are asked to enlarge the given triangle by a scale factor of \( 0.5 \), using the point \( (3, 1) \) as the center of enlargement.

### Steps to Solve:
1. **Identify Coordinates of Triangle Vertices:**
   The given triangle has three vertices. From the image, the approximate coordinates of the vertices of the triangle are:
   - \( A(-3, 0) \)
   - \( B(0, 0) \)
   - \( C(0, 4) \)

2. **Apply the Enlargement Transformation:**
   Using the scale factor \( k = 0.5 \), and the center of enlargement \( (3, 1) \), we use the enlargement formula:
   \[
   (x', y') = \left(3 + k \cdot (x - 3), 1 + k \cdot (y - 1)\right)
   \]
   Where \( (x, y) \) are the coordinates of the original points, and \( (x', y') \) are the new coordinates after enlargement.

3. **Calculate the Enlarged Coordinates:**
   - For vertex \( A(-3, 0) \):
     \[
     A' = \left(3 + 0.5 \cdot (-3 - 3), 1 + 0.5 \cdot (0 - 1)\right) = (3 - 3, 1 - 0.5) = (0, 0.5)
     \]
   - For vertex \( B(0, 0) \):
     \[
     B' = \left(3 + 0.5 \cdot (0 - 3), 1 + 0.5 \cdot (0 - 1)\right) = (3 - 1.5, 1 - 0.5) = (1.5, 0.5)
     \]
   - For vertex \( C(0, 4) \):
     \[
     C' = \left(3 + 0.5 \cdot (0 - 3), 1 + 0.5 \cdot (4 - 1)\right) = (3 - 1.5, 1 + 1.5) = (1.5, 2.5)
     \]

4. **Plot the Enlarged Triangle:**
   The new vertices of the enlarged triangle are:
   - \( A'(0, 0.5) \)
   - \( B'(1.5, 0.5) \)
   - \( C'(1.5, 2.5) \)

You can now plot these points on the grid and connect them to form the enlarged triangle.

Would you like more details or any further clarification on this? 

Here are five questions to further explore the topic:
1. How would the enlargement differ if the scale factor was greater than 1?
2. What happens if the center of enlargement is inside the triangle?
3. Can a scale factor be negative? How would that affect the enlargement?
4. How does translation differ from enlargement in transformations?
5. What is the effect of enlarging a shape when the center of enlargement is at the origin?

**Tip:** When performing enlargements, always ensure that the center of enlargement and the scale factor are carefully applied to avoid errors in your transformations.

Enlarge the triangle by scale factor 0.5 using (3, 1) as the centre of enlargement.

Learn how to enlarge a triangle by a scale factor of 0.5 with (3, 1) as the center. This guide covers the steps and the mathematical formulas used in the transformation, suitable for students in Grade 8-10.

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