It depends on how long after the nine years of marriage the remarriage takes place. The Social Security Administration (SSA) does not require that the marriage have been continuous for 10 years; it can be "interrupted by a prior divorce, provided the remarriage took place no later than the calendar year immediately following the calendar year of the divorce." For details from the SSA, click here.
For more on how divorce and remarriage affect Social Security benefits, click here.
For more on Social Security benefits for spouses and children, click here.