Question

postulate #2: if two distinct lines intersect, then their intersection is exactly one point. postulate #3: if two distinct planes intersect, then their intersection is a line. postulate #4: if you have three distinct noncollinear points, then there is exactly one plane that contains them. what characteristic must three points have to determine a plane? the points are noncollinear the points are collinear the points have no size the points exist in a singular location

Explanation:

Step1: Analyze Postulate #4

Postulate #4 states that if you have three distinct noncollinear points, then there is exactly one plane that contains them.

Step2: Check each option

• Option "The points are noncollinear": Matches Postulate #4.
• Option "The points are collinear": If points are collinear, there are infinitely many planes passing through them (not exactly one as required to determine a unique plane).
• Option "The points have no size": This is a general property of points (by definition in geometry, points have no size) but does not address the condition for determining a plane.
• Option "The points exist in a singular location": This is not a valid geometric condition for determining a plane. A singular location for three points would mean they are the same point (but we need three distinct points for a plane - and even then, non - collinearity is key).

Answer:

The points are noncollinear