Question

What are the coordinates of he image of point $X$ under a reflection in the line $LM$?

Answer 1

We can clearly see from the figure that equation of $LM$ is $x=y.$

So, if a point $(x,y)$ is under reflection of $x=y$ then the coordinates of reflected point is $(y,x)$.

$X\equiv (3,2)$

Image of $X\equiv (2,3)$.