we know that
The point Q is the image of point P in the line mirror, such that PQ is perpendicular to the line mirror, and the mid point L of PQ lies on the line mirror
So
In this problem the line mirror is equal to
[tex] y=2 [/tex]
point P is [tex] (6,9) [/tex]
PQ is perpendicular to [tex] y=2 [/tex]
PQ is equal to [tex] x=6 [/tex]
the midpoint L is [tex] (6,2)[/tex]
the distance point L to point P is equal to
[tex] (9-2) = 7\ units[/tex]
the distance point L to point Q will be also [tex] 7\ units[/tex]
the coordinates of point Q is equal to
[tex] (6,2-7)= (6,-5) [/tex]
therefore
the answer is
[tex] Q(6,-5) [/tex]
see the attached figure to better understand the problem
