Let A(1,−2) and B(4,1) be two given points. A point P(h,k) is to be located such that
(1) the line through P and A is parallel to 2x−3y+1=0, and
(2) the line through P and B is perpendicular to x+4y−11=0.
a. (i) Find the slopes of the lines specified in conditions (1) and (2).
b. (ii) Using the two conditions, set up the system of equations satisfied by h and k.
c. (iii) Solve the system to obtain the coordinates of P.
d. (iv) Write the equation of the line joining A and P.