If the point $(1,2)$  is reflected through the origin and then through the line $x=y$, then the new co-ordinates of the point are

The image of the point $(1,2)$  with respect to the origin $(-1,-2)$. The image of the point $(x,y)$ with respect to the line $x=y$ is $(y,x)$. So the image of the point $(-1,-2)$ with respect to the line $(-2,-1)$