Geometry/Coordinate Geometry - Inverting
Dear Prof Azeem
What could be the Impact to different disciplines and applications
of mathematics if Point (x,y) is replaced with Point (y,x).
i.e. x coordinate = Horizontal axis
y coordinate = Vertical axis
Now instead of this standard convention, implement the following
i.e. x coordinate = Vertical axis
y coordinate = Horizontal axis
For examples :
1st Quadrant Point A(3,2) will become Point A(2,3)
2nd Quadrant Point B(-2,3) will become Point B(3,-2)
3rd Quadrant Point C(-3,-4) will become Point C(-4,-3)
4th Quadrant Point D(2,-3) will become Point D(-3,2)
i.e. because the Points are now represented as y,x instead of x,y,
the Plotting of Points A,B,C,D on graph paper will be now different.
Can there be any impact while plotting Graphs viz Sine,Cosine, Tangent waves etc, vector algebra and other applications of mathematics similar to Coordinate Geometry if Point F (x,y) is represented as Point F(y,x) ?
Awaiting your reply,
Thanks & Regards,
Prashant S Akerkar
Mapping a point (x,y) to (y,x) is equivalent to reflecting the point about the line y=x and is also equivalent to rotating the point 90 degrees about the origin. If you're interested in transformations in the plane, then mapping (x,y) to (y,x) will be of use to you.
Consider now a function in the plane, y=f(x). If you swap x and y, evidently you will still get the same transformations listed above. However, what you will obtain is the inverse of the function f. For instance, if you graph y=tan(x) then switch all the x's and y's, you will obtain the graph of arctan(x). (Restrictions on the domain and range will be necessary for most functions.)