Question

What is the minimum value? Thanks in advance.

Answer 1

`13`

Explanation:

Calling

`d_1(x,y) = sqrt((x-1)^2+y^2)` and
`d_2(x,1) = sqrt((x-6)^2+(y-12)^2)`

we have that

`d_1(x,y)` is the generic distance to the point `p_1 = (1,0)`
`d_2(x,y)` is the generic distance to the point `p_2 = (6,12)`

so

`min d_1+d_2 = norm(p_1-p_2) = sqrt((6-1)^2+12^2) = 13`