Final answer:
The imaginary line described is the midsagittal plane, a vertical plane dividing the body into equal right and left halves.
Step-by-step explanation:
An imaginary line down the center of the body that passes between the eyes and extends down through the navel is known as the midsagittal plane or median plane. This plane divides the body vertically into right and left halves. When referencing the abdominopelvic region, a different system involving quadrants or regions is used. The simpler quadrants approach, often used in medicine, divides the cavity with one horizontal and one vertical line that intersect at the patient's umbilicus (navel), creating four quadrants. However, the specific line described in the question refers to the midsagittal plane.