https://file.aiquickdraw.com/mathbot/file/1729017404727td52pbw3.jpg

The problem involves enlarging the given shape by a **scale factor of -2**, using **(1, 4)** as the center of enlargement. Let’s walk through how to calculate the new coordinates for vertices \(A'\) and \(B'\).

---

### **Step-by-Step Solution:**

1. **Understand the formula for enlargement:**
   - The formula to calculate the new coordinates after enlargement is:
     \[
     \text{New Point} = \left( \text{Centre of Enlargement} + \text{Scale Factor} \times (\text{Original Point} - \text{Centre of Enlargement}) \right)
     \]
   - In this case, the **Centre of Enlargement** is \( (1, 4) \), and the **scale factor** is \(-2\).

2. **Find the original coordinates:**
   - From the grid, we can read:
     - \( A(4, 5) \)
     - \( B(8, 3) \)

3. **Apply the formula:**

   **For vertex A:**  
   - Original coordinates: \( A(4, 5) \)
   - Using the center of enlargement \( (1, 4) \) and scale factor \( -2 \):
     \[
     A' = \left( 1 + (-2) \times (4 - 1), \, 4 + (-2) \times (5 - 4) \right)
     \]
     \[
     A' = \left( 1 + (-2) \times 3, \, 4 + (-2) \times 1 \right)
     \]
     \[
     A' = \left( 1 - 6, \, 4 - 2 \right) = (-5, 2)
     \]

   **For vertex B:**  
   - Original coordinates: \( B(8, 3) \)
   - Using the center of enlargement \( (1, 4) \) and scale factor \( -2 \):
     \[
     B' = \left( 1 + (-2) \times (8 - 1), \, 4 + (-2) \times (3 - 4) \right)
     \]
     \[
     B' = \left( 1 + (-2) \times 7, \, 4 + (-2) \times (-1) \right)
     \]
     \[
     B' = \left( 1 - 14, \, 4 + 2 \right) = (-13, 6)
     \]

4. **New Coordinates:**
   - \( A' = (-5, 2) \)
   - \( B' = (-13, 6) \)

---

### Final Answer:
- **Coordinates of \( A' \):** \( (-5, 2) \)  
- **Coordinates of \( B' \):** \( (-13, 6) \)

---

Would you like me to plot these points or explain further details?

---

### Related Questions:
1. What happens if the scale factor is positive instead of negative?
2. How do transformations behave when the center of enlargement is moved to the origin?
3. Can a scale factor greater than 1 ever reduce the size of the shape?
4. What would the coordinates be if the scale factor were \(-\frac{1}{2}\) instead of \(-2\)?
5. How does enlargement affect the area of a shape?

**Tip:** When working with negative scale factors, keep in mind that the image will appear on the **opposite side** of the center of enlargement.

This shape is being enlarged by a scale factor of -2, using (1, 4) as the centre. Work out the coordinates of vertices A' and B'.

Solve a transformation geometry problem involving the enlargement of a shape with a scale factor of -2, centered at (1, 4). This problem covers key concepts in transformations and geometry for Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation