The problem asks for the correct position of triangle $Z$, which is obtained by reflecting triangle $X$ across line $P$ to form triangle $Y$, and then reflecting triangle $Y$ across line $Q$ to get triangle $Z$.

Here's how we can approach this:

1. First Reflection (Triangle X to Y):

   • Triangle $X$ is reflected in line $P$. By looking at the provided diagrams, line $P$ is a vertical line, which suggests a horizontal shift.
   • The reflection should mirror the triangle across line $P$. This means triangle $Y$ should be symmetrical to triangle $X$, across this vertical line.

2. Second Reflection (Triangle Y to Z):

   • Triangle $Y$ is then reflected in line $Q$, which appears to be a horizontal line based on the images provided.
   • This reflection will flip triangle $Y$ vertically to produce triangle $Z$.

Now, analyzing the options:

• We expect triangle $Z$ to be positioned symmetrically to triangle $Y$, based on the reflection across line $Q$.

By visual inspection:

• The correct answer appears to be option C because it shows a reflection of triangle $Y$ across the horizontal line $Q$ after the vertical reflection from triangle $X$ to $Y$.

Would you like a more detailed breakdown of the reflection process?

Relative Questions:

1. How do reflections work across vertical and horizontal lines in coordinate geometry?
2. What properties of a triangle remain unchanged after reflection?
3. Can you generalize the rule for reflecting any shape across two perpendicular lines?
4. How do you identify the lines of reflection given a figure and its image?
5. How can multiple transformations, like reflections and rotations, affect a figure's orientation?

Tip:

When reflecting across a line, think of the line as a "mirror" and imagine folding the grid along that line to visualize where the image will appear.