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:
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(x, y) = (3, 5)
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| y
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——–+——– x
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(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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