Why must the x and y axis be perpendicular?

[Phillipv2004]

Homework Statement

I have a conceptual question regarding why the x and y-axis must be perpendicular. Chapter 2 in section 2-1 of Giancoli's Physics states that " The x and y axes are always perpendicular". This chapter is one-dimensional motion and the section is Reference frames and Displacement.

Homework Equations

The Attempt at a Solution

 

[fresh_42]

Homework Statement

I have a conceptual question regarding why the x and y-axis must be perpendicular. Chapter 2 in section 2-1 of Giancoli's Physics states that " The x and y axes are always perpendicular". This chapter is one-dimensional motion and the section is Reference frames and Displacement.

Homework Equations

The Attempt at a Solution

It is a convention, not a necessity. It makes calculations a lot easier as if the angle was another, but it is not a must. However, if you say $x,y$ coordinates, everybody around the world will assume perpendicular axis. So it you should use others, please tell.

 

[Bandersnatch]

They are perpendicular because that's how the Cartesian coordinate system is defined. In general, they don't have to be, in the sense that one can define a coordinate system in N dimensions consisting of N linearly independent basis vectors that can be at any angle w/r to each other. So for example in 2 dimension you could have a coordinate system defined by two vectors at 45° to each other, and still be able to uniquely name any position on this 2D plane as well as convert to the Cartesian coordinates.
But the Cartesian coordinate system is conventionally used in much of physics, and it requires the axes to be at 90° by definition.

The topic of vector bases is covered by linear algebra, so if you are going to be taking those classes, it'll all be explained there.