-reflected-over-the-x-axis.jpeg "(2 5) Reflected Over The X Axis")
Reflecting a Graph over the x-axis: A Comprehensive Guide
Reflecting a graph over the x-axis is a fundamental concept in algebra and graphing. In this article, we will explore what happens when we reflect the graph of the equation (2, 5) over the x-axis.
What is Reflection over the x-axis?
Reflection over the x-axis is a transformation that flips the graph of a function over the x-axis. In other words, it mirrors the graph across the x-axis. This transformation can be represented algebraically by multiplying the y-coordinate of each point on the graph by -1.
Reflecting the Graph of (2, 5)
Let's take the point (2, 5) and reflect it over the x-axis. To do this, we will multiply the y-coordinate (5) by -1, resulting in -5. The x-coordinate (2) remains the same. Therefore, the reflected point is (2, -5).
Graphical Representation
Here is a graphical representation of the reflection:
+---------------+
| |
| (2, 5) |
| |
+---------------+
|
|
v
+---------------+
| |
| (2, -5) |
| |
+---------------+
As you can see, the point (2, 5) has been reflected over the x-axis to become (2, -5).
Properties of Reflection over the x-axis
Here are some important properties of reflection over the x-axis:
- The x-coordinate remains the same.
- The y-coordinate is multiplied by -1.
- The graph is flipped over the x-axis.
- The reflection of a point is its mirror image across the x-axis.
Conclusion
In conclusion, reflecting the graph of (2, 5) over the x-axis results in the point (2, -5). This transformation is a fundamental concept in algebra and graphing, and it has many applications in mathematics and real-world problems. By understanding the properties of reflection over the x-axis, we can better analyze and interpret graphical representations of functions.
