To map triangle $F$ onto triangle $G$, we need to apply two transformations. Let’s analyze the steps:

1. Reflection in line $x = 1$:

   • Reflecting triangle $F$ (currently right of $x = 1$) across $x = 1$ would place it symmetrically on the left side of the line, closer to the position of triangle $G$.

2. A translation by vector $\begin{pmatrix} -4 \\ 0 \end{pmatrix}$:

   • After reflection, translating the triangle leftward by 4 units along the $x$-axis aligns triangle $F$ perfectly with triangle $G$.

Final Transformations:

1. Reflection in line $x = 1$
2. Translation by vector $\begin{pmatrix} -4 \\ 0 \end{pmatrix}$

Does this make sense? Let me know if you’d like a detailed explanation of each transformation or need further assistance!

Here are 5 related questions to expand your understanding:

1. What is the effect of reflecting a shape across a vertical or horizontal line?
2. How can you determine the vector needed to translate a shape to a specific location?
3. What happens when a shape undergoes a rotation around a point?
4. How does an enlargement transformation affect the size and position of a shape?
5. Can a combination of reflections and rotations produce the same result as a translation?

Tip: When solving transformation problems, always note down the coordinates of key points before and after each transformation!