The question asks for the coordinates of the vertices of triangle $X''Y''Z''$ after it is reflected across the $x$-axis.

Step 1: Reflection Rule

When a point $(x, y)$ is reflected across the $x$-axis, the resulting point is $(x, -y)$.

Step 2: Original Coordinates of $X, Y, Z$

From the graph:

• $X(-1, 6)$
• $Y(-4, 1)$
• $Z(-6, -3)$

Step 3: Applying the Reflection Rule

• Reflect $X(-1, 6)$: $X''(-1, -6)$
• Reflect $Y(-4, 1)$: $Y''(-4, -1)$
• Reflect $Z(-6, -3)$: $Z''(-6, 3)$

Final Coordinates of $X''Y''Z''$

• $X''(-1, -6)$
• $Y''(-4, -1)$
• $Z''(-6, 3)$

Let me know if you'd like me to provide more details about reflections, or clarify further!

Here are 5 related questions to deepen your understanding:

1. What happens when a triangle is reflected across the $y$-axis instead of the $x$-axis?
2. How do you find the coordinates of a point after a reflection over the line $y = x$?
3. What would the coordinates of $X''Y''Z''$ be if reflected across both axes?
4. How can you verify the accuracy of a reflection transformation on a graph?
5. How does reflecting a figure change its orientation?

Tip: Always double-check your transformations by sketching both the original and reflected figures on a graph.