# 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?

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