Coordinate question

The red line represents the equation $y=2x+5$.

The bue point represents the point$(6,2)$

The green line represents the line that is perpendicular to the red line, while crossing the blue point. 

The reflection must be a point on the green line that has an x-intercept at $-6$ ($6$ units to the left of the intersection, since the blue point is $6$ units to the right)

This means that the reflection is at $\color{brown}\boxed {(-6,8)}$