If so, then find the slope of the line 4x + 3y + 6 = 0 (by solving for "y=" and then reading off the value of "m"). Find the equation of the line through (1, 5) and having a slope that is perpendicular to the original line.
Now that you have two line equations, you have a system of equations. Solve this system to find where the two lines cross. The intersection point is the closes point on the line to the point (1, 5).
Plug the original point and the intersection point into the Midpoint Formula, using (x, y) as the point equidistant on the other side, and solve for the coordinates of the image (mirrored) point.
If you get stuck, please reply showing all of your steps and reasoning so far. Thank you!