Of course you can do this. Historically x and y are mostly assumed orthogonal (cartesian coordinate system.) as I stated in the picture, and in this example they are certainly not. Also, by convention, if you use more than a few generalized variables, you run out of letters quickly (x,y,z,.....) therefore it was decided (a long time ago) that x_1,x_2,x_3 or x^1, x^2, x^3 (no powers!! but indices) was a better approach to refer to variables. But in this case because the problem is relatively simple you are right and you can use x and y. I hope this helps.
why don't you simply use x and y in place of x1 and x2 ?
Of course you can do this. Historically x and y are mostly assumed orthogonal (cartesian coordinate system.) as I stated in the picture, and in this example they are certainly not. Also, by convention, if you use more than a few generalized variables, you run out of letters quickly (x,y,z,.....) therefore it was decided (a long time ago) that x_1,x_2,x_3 or x^1, x^2, x^3 (no powers!! but indices) was a better approach to refer to variables. But in this case because the problem is relatively simple you are right and you can use x and y. I hope this helps.
I don’t understand why it is x_2 sin theta for y coordinate, shouldn’t it be x_1 sin theta?