Java interview test

This morning in a work interview they asked me if I get a some legacy code with no tests at all, and I need to modify something, how would I do it to be completely sure that I break nothing.

My answer was, first of all I would create a test for the part of the code I need to modify, then once the test is passing, I would do the modification of the code ensuring that the test is still passing. So basically doing it from a test driven development approach. I did not see the the person interviewing me really ok with myanswer so, I would like to have your opinions on the subjects, there are better approaches for that?

Is it valid my answer?

Thank you very much