To determine which sequence of transformations maps triangle ABC to triangle GHI, let's analyze the options step by step:

Observations

• Triangle ABC is located in Quadrant I.
• Triangle GHI is located in Quadrant III.
• The triangles appear to have the same size and orientation but are reflected and shifted.

Solution Process

1. First Reflection:

   • Reflecting across the x-axis takes a point $(x, y)$ to $(x, -y)$, flipping it vertically.
   • This reflection moves Triangle ABC closer to Quadrant III, but it is still in Quadrant IV.

2. Translation:

   • Translating 4 units to the left moves points horizontally to the left: $(x, y) \to (x - 4, y)$.

Testing Option B

Option B states:

• A reflection across the x-axis followed by a translation of 4 units to the left.

Step 1: Reflect across the x-axis

For points:

• $A(3, 4) \to A'(3, -4)$
• $B(5, 1) \to B'(5, -1)$
• $C(2, 1) \to C'(2, -1)$

The triangle now lies in Quadrant IV.

Step 2: Translate 4 units to the left

Move each point:

• $A'(3, -4) \to A''(-1, -4)$
• $B'(5, -1) \to B''(1, -1)$
• $C'(2, -1) \to C''(-2, -1)$

These are the coordinates of Triangle GHI:

• $G(-1, -4)$
• $H(1, -1)$
• $I(-2, -1)$.

Verification

The sequence in Option B perfectly matches Triangle GHI.

Final Answer:

B. A reflection across the x-axis followed by a translation of 4 units to the left.

Do you want me to clarify any step or show another transformation approach?

Here are 5 related questions:

1. How do you reflect a shape across the y-axis?
2. What are the coordinates of a point rotated 90° about the origin?
3. How do you combine multiple transformations on the coordinate plane?
4. What happens when you reflect across both axes?
5. Can a single transformation map a figure into another quadrant?

Tip: Always apply transformations step-by-step and check coordinates after each move.