How to prove a midpoint? (coordinate geometry) (1 Viewer)

[Manylearn]

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 can't do the proof for XY being perpendicular because that is part (b) of the question.

So for example if I said that a=3 and b=5, then X(3,5) and Y(5,3). I can easily find the distance and midpoint of the the line and therefore prove that M lies on the point (4,4) which is indeed on the line y=x, but since this is a proof I don't think I should be giving values to a and b?

I would really appreciate any feedback/help!

 

[Carrotsticks]

Have you tried finding the coordinates of M yet?

When you do so, you will soon see the solution...

 

[Manylearn]

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

 

[Manylearn]

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?

 

[RealiseNothing]

Would it be correct if I said (x,y) = (a+b/2 , b+a/2) therefore x = y

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[RealiseNothing]

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

No.