Reflection Over Y = X: A 90-Degree Rotation Counterclockwise About The Origin

Reflection over y = x

Exchange the x and y values; (x,y) -> (y,x)

When we talk about reflection over y = x, we’re referring to a transformation in coordinate geometry where each point (x, y) is transformed to the point (y, x). In other words, we’re swapping the x and y-coordinates of each point. This transformation is also known as a 90-degree rotation counterclockwise about the origin.

To better understand this concept, let’s consider an example. Suppose we have a point A(3, 5). If we reflect this point over y = x, we swap its x and y-coordinates, so its reflection will be A'(5, 3). We can see this transformation in the diagram below:

“`
(x, y) = (3, 5)
|
| y
| |
| |
| |
——–+——– x
| |
| |
| |
| |
(y, x) = (5, 3)
“`

Here, we can see that the reflection over y = x is a 90-degree rotation counterclockwise about the origin. We can also see that any point on the line y = x will remain fixed under this transformation, since swapping the x and y-coordinates will give us the same point.

Overall, reflection over y = x is a useful tool in geometry, and it can help us better understand certain concepts and relationships between different points and shapes on a coordinate plane.

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