Yes, but how is it geometrically?

Algebra Level 5

If \({ z }_{ 1 }=10i,\quad { z }_{ 2 }=11+12i,\quad { z }_{ 3 }=x\) where \(x\) is a real number, then what must be the value of \(x\) for \(\left| { z }_{ 2 }-{ z }_{ 3 } \right| +\left| { z }_{ 1 }-{ z }_{ 3 } \right| \) to be at its minimum value?

[..This question is not original..]

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