On a city map, one unit represents one metre. A straight road is represented by the line 5x−12y+60=0. A fountain is located at F(8,−2). A walkway is to be built from the fountain perpendicular to the road, meeting the road at G, and is then to be extended beyond G in the same straight line to reach a point H such that GH=15m.
(i) Find the equation of the straight line representing the walkway segment FG.
(ii) Determine the coordinates of the point G where the walkway meets the road.
(iii) Calculate the shortest distance from the fountain to the road.
(iv) Obtain the coordinates of the point H on the extension of FG if GH=15m.