In the given slide on 4.2 Reflections, the problem involves reflecting Triangle P over the x-axis to create its image, Triangle Q. Let’s analyze the reflection rule:

Rule for reflection over the x-axis

When a point $(x, y)$ is reflected over the x-axis, its coordinates become: $(x, y) \rightarrow (x, -y)$

This means:

1. The x-coordinate stays the same.
2. The y-coordinate becomes its opposite (sign flips).

Identifying the correct graph:

By looking at the options on the slide:

• Triangle Q is vertically "flipped" relative to Triangle P.
• This matches the rule above.

The correct graph would be the one where Triangle P and Triangle Q have the same x-values, but the y-values are negated.

Let me know if you’d like me to:

1. Analyze each option graphically in detail.
2. Explain further reflections across other axes or lines.
3. Solve any related practice problems.

Related Questions:

1. What is the rule for reflecting a point over the y-axis?
2. How do you reflect a point across the line $y = x$?
3. If a triangle is reflected twice (e.g., over the x-axis and then the y-axis), what happens to its coordinates?
4. Can you describe a real-life example where reflections are used?
5. What is the effect of combining reflections with other transformations, such as translations?

Tip:

When reflecting over the x-axis, always focus on the y-values — flipping the sign while keeping x-values constant simplifies the process.