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.