Question

"Through three points there exists one line."

What word, when substituted for the highlighted word in the previous sentence, corrects a possible error in the postulate?

Answer 1

"Though three points there exists one line."---Incorrect Statement

→"Though two points there exists one line."

This can be explained in the following way.To determine a unique line we need only two points.

→If a line passes through three points, it means these three points are collinear.

Answer 2

Through any three non collinear points(The points which do not lie on the same line ), there exists exactly one plane.

Explanation:

We have given the postulate:

"Through three points there exists one line."

According to the three point postulate:

Through any three non collinear points(The points which do not lie on the same line ), there exists exactly one plane.

Through three non-collinear points X,Y,Z there exists exactly one plane.

The plane XYZ contains atleast three non collinear points...