Is it legal to leave 17 year-old home alone for 10 days?

Of course it is legal to let a 17 year old stay alone for this period of time. The age of consent is 17 in New York and for all intensive purposes he/she is an adult. Now, this is assuming the person is not suffering from any mental disorder or incapacity that would negate this. I am not quite sure of what the situation is that you need this answered since you characterize this as a personal injury question. I am not sure what actually happened while this person was left home so without more information I cannot give you a better answer. However, you did nothing wrong by leaving him/her alone provided they did not suffer from any mental illness or malady.