To solve the problem:

Given:

You are reflecting the triangle $\triangle ABC$ over the x-axis. The reflection rule states: $(x, y) \rightarrow (x, -y)$

Steps:

1. Apply the reflection rule to the given points:
   • $A(-1, -3) \rightarrow A'(-1, 3)$
   • $B(-2, 4) \rightarrow B'(-2, -4)$
   • $C(1, 5) \rightarrow C'(1, -5)$

Final Answer:

• Reflected Points:

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

• Next Step: Plot these new points $A', B', C'$ on the graph.

Let me know if you want a detailed explanation of how reflection works or anything else. Here are some related questions to deepen your understanding:

Related Questions:

1. What is the reflection rule for a line other than the x-axis (e.g., y-axis or diagonal)?
2. How do you find the equation of a line of reflection given two corresponding points?
3. Can you derive a formula for reflecting over the y-axis?
4. How does reflection affect the orientation of shapes?
5. What happens to the coordinates when reflecting across $y = x$?

Tip:

When reflecting a shape over the x-axis, only the y-coordinate changes sign while the x-coordinate stays the same.