Find the minimum value of $$P(z) = |2z-1-i|+|3z-2-2i|+|4z-3-3i|$$ where z is a complex number
My try: I have done this kind of questions and I know the approach is using coordinates. so it can be written as $$2|z-\frac{1+i}{2}|+3|z-\frac{2(1+i)}{3}|+4|z-\frac{3(1+i)}{4}|$$
all three points $(\frac{1}{2},\frac{1}{2}), (\frac{2}{3},\frac{2}{3}), (\frac{3}{4},\frac{3}{4})$ lie on line $y=x$ so I am able to conclude that required point (for minimum) will also lie on same line. But I am not able to proceed further, please guide me how to deal with coefficients.