To solve this problem, we'll need to analyze the sequence of transformations given for each line segment.

Given Transformations:

1. Reflection $(x, y) \rightarrow (x, -y)$
2. Reflection $(x, y) \rightarrow (-x, y)$
3. Reflection $(x, y) \rightarrow (y, x)$

Steps:

1. Analyze Line CD:

   • The original line $CD$ is the red line with coordinates $C(-5, -3)$ and $D(-1, -6)$.

2. Apply the First Transformation: Reflection $(x, y) \rightarrow (x, -y)$:

   • Reflecting each point:
     • $C(-5, -3) \rightarrow C'(-5, 3)$
     • $D(-1, -6) \rightarrow D'(-1, 6)$
   • This gives us a line segment $C'D'$ with the new coordinates $C'(-5, 3)$ and $D'(-1, 6)$.

3. Apply the Second Transformation: Reflection $(x, y) \rightarrow (-x, y)$:

   • Reflecting each point:
     • $C'(-5, 3) \rightarrow C''(5, 3)$
     • $D'(-1, 6) \rightarrow D''(1, 6)$
   • This gives us a line segment $C''D''$ with the new coordinates $C''(5, 3)$ and $D''(1, 6)$.

4. Apply the Third Transformation: Reflection $(x, y) \rightarrow (y, x)$:

   • Reflecting each point:
     • $C''(5, 3) \rightarrow C'''(3, 5)$
     • $D''(1, 6) \rightarrow D'''(6, 1)$
   • This gives us a line segment $C'''D'''$ with the new coordinates $C'''(3, 5)$ and $D'''(6, 1)$.

Matching with Given Options:

• The sequence we've derived corresponds to the green line segment $EF$ in the graph, which matches the transformation sequence in option c.

Answer: Option c. CD → EF → AB → GH.

Would you like more details or have any questions?

Here are 5 related questions for practice:

1. What would be the effect of rotating $CD$ by 90 degrees counterclockwise instead of reflecting?
2. How would the transformation change if the sequence was done in reverse order?
3. Can you identify which transformation sequence would result in mapping CD to AB directly?
4. What would happen if we only applied the first and last transformations?
5. How does each reflection transformation affect the slope of the line segment?

Tip: Always remember to check the order of transformations, as it greatly affects the final result.