Which statements are true regarding undefinable terms in geometry? Check all that apply.

Question

A point has no length or width.
A point indicates a location in a coordinate plane.
A plane has one dimension, length.
A line has a definite beginning and end.
A plane consists of an infinite set of lines.
A line consists of an infinite set of points.

Answer 1

Let's evaluate each statement regarding undefinable terms in geometry:

1. A point has no length or width. - True: By definition, a point is considered to have no dimension—neither length, width, nor height.

2. A point indicates a location in a coordinate plane. - True: A point can indeed indicate a specific location in a coordinate plane, usually represented by ordered pairs (x, y).

3. A plane has one dimension, length. - False: A plane actually has two dimensions: length and width.

4. A line has a definite beginning and end. - False: A line is defined as a straight path that extends infinitely in both directions, meaning it does not have a definite beginning or end.

5. A plane consists of an infinite set of lines. - True: A plane can be thought of as containing an infinite number of lines that can be drawn in that two-dimensional space.

6. A line consists of an infinite set of points. - True: A line is composed of an infinite number of points stretched out along its length.

Based on this evaluation, the true statements are:

• A point has no length or width.
• A point indicates a location in a coordinate plane.
• A plane consists of an infinite set of lines.
• A line consists of an infinite set of points.