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