0.5 Reflected Over the Y-Axis
What is Reflection?
In geometry, a reflection is a transformation that flips a figure over a line, called the axis of reflection. The resulting figure is a mirror image of the original figure.
Reflection Over the Y-Axis
When we reflect a point or a figure over the Y-axis, we are flipping it over the vertical line x = 0. This means that the x-coordinate of each point changes sign, while the y-coordinate remains the same.
Reflection of 0.5
Let's consider a point with coordinates (0.5, y), where y is any real number. To reflect this point over the Y-axis, we need to change the sign of the x-coordinate.
New Coordinates
The new coordinates of the reflected point will be (-0.5, y). Notice that the x-coordinate has changed sign, while the y-coordinate remains the same.
Graphical Representation
Here's a graphical representation of the reflection:
Before Reflection:
(0.5, y)
After Reflection:
(-0.5, y)
Properties of Reflection
Reflection over the Y-axis has several important properties:
- The distance between the original point and the Y-axis is equal to the distance between the reflected point and the Y-axis.
- The reflected point is on the opposite side of the Y-axis from the original point.
- The y-coordinate of the reflected point is the same as the y-coordinate of the original point.
Real-World Applications
Reflection over the Y-axis has many real-world applications, such as:
- Symmetry in art and design: Reflection is used to create symmetrical designs and patterns.
- Geometry and trigonometry: Reflection is used to solve problems involving right triangles and trigonometric identities.
- Physics and engineering: Reflection is used to model the motion of objects in physics and engineering.
In conclusion, reflecting 0.5 over the Y-axis results in a new point with coordinates (-0.5, y). This transformation has many applications in geometry, trigonometry, physics, and engineering.
