Let P(5,7) be a point and let the line l be given by 3x+4y−12=0.
(i) Obtain the equation of the straight line passing through P and perpendicular to l.
(ii) Find the coordinates of the point Q at which this perpendicular line meets l.
(iii) Calculate the length of the segment PQ.
(iv) Verify by computation that the product of the slopes of the two lines is −1.