https://file.aiquickdraw.com/mathbot/file/17318024309699dvzqi8c.jpg

The problem involves the vertices of triangle \( \triangle ABC \) at points \( A(2, 2) \), \( B(4, 2) \), and \( C(3, 4) \), and the task is to apply the transformation \( (x, y) \to (x + y, y) \).

### Transformation Process:
1. **Transform each vertex** using the given rule:
   - For \( A(2, 2) \): 
     \[
     (x, y) \to (x + y, y) = (2 + 2, 2) = (4, 2)
     \]
   - For \( B(4, 2) \): 
     \[
     (x, y) \to (x + y, y) = (4 + 2, 2) = (6, 2)
     \]
   - For \( C(3, 4) \): 
     \[
     (x, y) \to (x + y, y) = (3 + 4, 4) = (7, 4)
     \]

2. **New vertices of \( \triangle ABC \):**
   - \( A'(4, 2) \), \( B'(6, 2) \), \( C'(7, 4) \).

### Explanation of the Transformation:
This is a **translation**, as each point's \( x \)-coordinate is adjusted by adding the corresponding \( y \)-value while the \( y \)-coordinate remains unchanged. This results in a consistent shift in the graph without altering the shape or orientation of the triangle.

### Correct Answer:
- **Yes, the figure is translated to the right.**

Would you like further clarification or visualization of the transformation? Here are related questions to expand your understanding:

1. What happens to the shape of \( \triangle ABC \) under different types of transformations (e.g., rotations, reflections)?
2. How would the transformation \( (x, y) \to (x - y, y) \) affect the triangle's position?
3. What are the algebraic conditions for a transformation to be a translation?
4. Could you describe the differences between translations, dilations, and reflections geometrically?
5. How does this transformation affect the distances between the vertices of the triangle?

**Tip:** When analyzing transformations, focus on how \( x \) and \( y \) coordinates are modified to predict geometric changes efficiently.

The vertices of triangle ABC are A(2, 2), B(4, 2), and C(3, 4). Apply the transformation (x, y) → (x + y, y) and determine the new vertices of the triangle. Is this transformation a translation? Explain your reasoning.

Learn how to transform triangle ABC with vertices A(2, 2), B(4, 2), and C(3, 4) using the transformation (x, y) → (x + y, y). Understand whether this transformation is a translation and its effect on the shape and orientation of the triangle. Suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation