The diagnostic test performed to determine the size, position, and patency of the uterus and fallopian tubes is:

Hysterosalpingography is the diagnostic test that determines the size position, and patency of the uterus and fallopian tubes. It is primarily used to examine the uterus and fallopian tubes of a woman who is having difficulty of becoming pregnant. It's also used to investigate miscarriages resulting from uterine abnormalities, to determine the presence and severity of tumor masses, adhesion and fibroids. Occasionally, hysterosalpingography can open blocked fallopian tubes to allow patients to become pregnant afterwards.