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
\(y=2\)
point P is \((6,9)\)
PQ is perpendicular to \(y=2\)
PQ is equal to \(x=6\)
the midpoint L is \((6,2)\)
the distance point L to point P is equal to
\((9-2) = 7\ units\)
the distance point L to point Q will be also \(7\ units\)
the coordinates of point Q is equal to
\((6,2-7)= (6,-5)\)
therefore
the answer is
\(Q(6,-5)\)
see the attached figure to better understand the problem
