Let's look at how reflection axes work

The point you're reflecting, let's call it (X,Y)

Your reflection axis is a straight line, **0=ax+by+c**

In this specific case it's **0=1x-1y**

The direction **perpendicular** to this axis is **(1,-1)** which is 45° southeast

If (X,Y) moves into this direction a certain amount **K**, the point will land on the reflection axis itself

(X,Y) + K·(1,-1) = (X+K, Y-K)

is on the axis

0 = x - y

0 = X+K - (Y-K)

0 = X-Y + 2K

2K = Y-X

K = (Y-X)/2

But you want to move twice that amount so you get reflected to the other side

(X,Y) + 2K·(1,-1) = (X+2K, Y-2K)

is on the other side

Xnew = X + 2K Ynew = Y - 2K

= X + 2(Y-X)/2 = Y - 2(Y-X)/2

= X + Y-X = Y + X-Y

= Y = X