Find Weight for minimum Manhattan Distance Let's say, I have three points $(1, 4)$, $(4, 3)$ and $(5, 2)$. I need to find weight $w_1$ and $w_2$ so that the point $(1, 4)$ be the centroid of the points in Manhattan Distance. Actually, the point $(1, 4)$ must have the minimum total distance from others.
How can I weight those X and Y coordinates to minimalize the total distance toward point $(1, 4)$? 

Rescale $x$-coordinates with $(2/9)$ and $y$-coordinates with $(8/5)$, giving:
$$
   \left(\frac{2}{9}\times 4,\frac{8}{5} \times 3 \right) = \left( \frac{8}{9} , \frac{24}{5} \right) \qquad ; \qquad \left(\frac{2}{9}\times 5,\frac{8}{5} \times 2 \right) = \left( \frac{10}{9} , \frac{16}{5} \right)
$$
Centroid = $(9/9,20/5)$ .
