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Would it be correct if I said (x,y) = (a+b/2 , b+a/2) therefore x = y, and since the line y=x has a gradient of 1 i.e points are 2,2 3,3 4,4 and so on, then M lies on the line y=x?

Yeah I thought I could do that but is it ok to give values to a and b in a proof?

I have been given this question in an assignment X(a,b) and Y(b,a) are points on a number plane and M is the midpoint of XY. Prove that M lies on the line y=x I know what they're asking and you can see that whatever value you give to a and b the line XY will be perpendicular to y=x. But I...