https://file.aiquickdraw.com/mathbot/file/1726593852917toqrbode.jpg

To solve this problem, we are looking for the new position of vertex \( V \) after the trapezium is enlarged by a scale factor of 3, with the center of enlargement at the red cross (marked as \( \times \)).

### Step-by-step solution:
1. **Identify the coordinates of the center of enlargement and vertex \( V \):**
   - The red cross (center of enlargement) appears to be at the point \( (2, -2) \).
   - Vertex \( V \) is at \( (5, 0) \).

2. **Calculate the vector from the center of enlargement to vertex \( V \):**
   The vector from \( \times \) to \( V \) is obtained by subtracting the coordinates:
   \[
   (5, 0) - (2, -2) = (3, 2)
   \]
   So the vector from the center to vertex \( V \) is \( (3, 2) \).

3. **Enlarge this vector by a scale factor of 3:**
   To apply the enlargement, multiply the vector \( (3, 2) \) by 3:
   \[
   3 \times (3, 2) = (9, 6)
   \]

4. **Find the coordinates of the new vertex:**
   To get the coordinates of the new vertex that corresponds to \( V \), add this scaled vector to the coordinates of the center of enlargement:
   \[
   (2, -2) + (9, 6) = (11, 4)
   \]

5. **Conclusion:**
   The new position of the vertex corresponding to \( V \) is at \( (11, 4) \), which corresponds to point \( D \) on the diagram.

Thus, the letter marking the position of the vertex corresponding to \( V \) is \( D \).

Would you like a further breakdown of any step, or do you have any questions?

### 5 related questions:
1. How do you calculate an enlargement transformation for different shapes?
2. What happens to the angles of a shape during an enlargement transformation?
3. How can you determine the scale factor in an enlargement if it's unknown?
4. How do different types of transformations (reflection, rotation, and enlargement) differ in terms of geometry?
5. How does the position of the center of enlargement affect the resulting image?

### Tip:
Always make sure to subtract coordinates in the correct order when calculating vectors during transformations!

This trapezium is being enlarged by a scale factor of 3 with the centre of the enlargement at the cross. Which letter marks the position of the vertex of the new trapezium that corresponds to vertex V?

Solve the enlargement problem where a trapezium is scaled by a factor of 3. Learn how to calculate the new vertex position using vector transformations, with a focus on geometric enlargement. Suitable 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