doubt in minimum value

[man111]

find Min. value of [tex]\sqrt{x^2+4}+\sqrt{(y-x)^2+4}+\sqrt{(y-14)^2+1}[/tex]

and answer is Given as

but my doubt is that why we can not take point [tex]C(14,3)[/tex] instead of [tex]C(14,5)[/tex]

because When We take [tex]C(14,3)[/tex]. Then Minimum is =[tex]\sqrt{205}[/tex]

but here answer is =[tex]\sqrt{221}[/tex]

explanation required

[drago]

Yes, You can interpret the last term as distance to the point (14,3), but You can't arange two varying points (x,2) , (y,4) to be on the segment ) (0,0) (14, 3). The point (y,4) can lie on the line (0,0) (14,3) but outside these two points, so the min value is greater than [tex]\sqrt{205}[/tex].