A triangle has vertices at coordinates $(1, 2), (7, 10)$ and $(1, 12)$.  What is the number of units in the length of the shortest side of the triangle?
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
A triangle has vertices at coordinates $(1, 2), (7, 10)$ and $(1, 12)$.  What is the number of units in the length of the shortest side of the triangle?
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
2\sqrt{10}
A triangle has vertices at coordinates $(1, 2), (7, 10)$ and $(1, 12)$.  What is the number of units in the length of the shortest side of the triangle?
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