The problem asks you to reflect the given point $H$ over the $x$-axis to find the coordinates of $H'$, the reflected point.

Key Rule for Reflection Over the $x$-axis:

When a point $(x, y)$ is reflected over the $x$-axis:

• The $x$-coordinate remains the same.
• The $y$-coordinate changes its sign (positive to negative or negative to positive).

Given Coordinates of $H$:

From the graph:

• The coordinates of $H$ are $(2, 4)$.

Reflected Coordinates of $H'$:

• $x' = x = 2$ (same $x$-coordinate)
• $y' = -y = -4$ (sign of $y$ changes)

So, the coordinates of $H'$ are: $H' = (2, -4)$

Final Answer:

You would plot $H'$ at the point $(2, -4)$ on the graph.

Would you like additional details on how reflections work or more practice? Let me know! Below are related questions you can explore.

Related Questions:

1. What happens to the coordinates of a point when it is reflected over the $y$-axis?
2. How can we reflect a point across both axes simultaneously?
3. What is the general rule for reflecting a point over the line $y = x$?
4. How would the reflection change if the point were below the $x$-axis initially?
5. What are the coordinates of a point after being reflected twice (over $x$-axis and $y$-axis)?

Tip:

To quickly verify reflections, plot both the original point and its reflection to ensure they are symmetric about the line of reflection (in this case, the $x$-axis).