Explanation:

To understand the answer to this question, we need to first define what a line is in geometry. In geometry, a line is a straight path that extends infinitely in both directions. It is made up of infinitely many points.

Now, let's consider the given scenario where we have a plane and two distinct points. A plane is a flat surface that extends infinitely in all directions. It is a two-dimensional object.

Definition of a line segment:
A line segment is a part of a line that is bounded by two distinct points. It has a definite length.

Connecting two distinct points:
When we connect two distinct points in a plane, we are essentially drawing a line segment between them. This line segment is a straight path that connects the two points and has a definite length.

Number of lines that can be drawn:
According to the question, we need to determine how many lines can be drawn between the two distinct points. Since a line is made up of infinitely many points, we can only draw one line between the two distinct points.

Explanation of the options:
a) Two: This option is incorrect because we can only draw one line between the two distinct points.
b) One: This option is correct as it accurately represents the number of lines that can be drawn between two distinct points in a plane.
c) Zero: This option is incorrect because we can always draw a line between two distinct points in a plane.
d) Infinitely many: This option is incorrect because we can only draw one line between the two distinct points.

Therefore, the correct answer is option 'B' - One.