What is this and why is it so important $(x,y) \to (y,x)$?

Question

When doing a $y=x$ reflection the notation is $(x,y) \to (y,x)$. My teacher told us to find out what it is, what it is called, and why it is important? Please help ?

Answer 1

The reflection of points on a plane (with coordinates $(x,y)$) across the axis (in this case, the line described by the equation $y=x$) is just the mapping $(x,y)\to(y,x)$. For example, the reflection (the mirror image) of the point $(1,3)$ across the line $y=x$ is the point $(3,1)$. (Click on the highlighted terms for more information.)

Answer 2

This is the general formula for translating graphs (or anything else placed on the coordinate axis) across the line y=x. For example, you would mirror the point (4,3) across the line y=x to the point (3,4).

Answer 3

This mapping creates the inverse relation (or inverse function, if the original is a bijective function).