#### Answer

The statement is false.
A corrected statement is:
"If the product of a point's coordinates is positive, the point must either be in Quadrant I or Quadrant III."

#### Work Step by Step

The statement is false.
The product of two numbers is positive if they have the same signs.
This means that the coordinates of a point such as $(-1, -1)$, which is in Quadrant III, also has a positive product.
A corrected statement is:
If the product of a point's coordinates is positive, the point must either be in Quadrant I or Quadrant III.