12.3.2.3 Geometric

Condition: Find all pairs of numbers \ ((x, y) \), for which the expression \ [\ begin {array} {l} \ sqrt {(x-2)^{2}+y^}+\ sqrt {x^{2}+(y-4)^{2}}+\\+\\+\\+\\+\\+\\+\\ +\ sqrt {(x-4)^{2}+(y-3)^{2}}+\ sqrt {(x+2)^{2}+(y-1)^} \ end {arry} \] take the minimum value.