Question

Which statements are true regarding undefinable terms in geometry?

Select two options.

• A. A point's location on the coordinate plane is indicated by an ordered pair $\left(x,y\right)$
  
• B. A point has one dimension, length.
• C. A line has length and width.
• D. A distance along a line must have no beginning or end.
• E. A plane consists of an infinite set of points.

Answer 1

Answer: (A), (E)

A plane consists of an infinite set of points.

The explanation for the correct option:

Option $\left(A\right)$:

• Geometry's three undefined terms are as follows: Point, Line, and Plane.
• For example, Point cannot be defined specifically but can be used to define any 2D or 3D objects in cartesian space, such as a triangle, line segment, or cube. Similarly, a line is just another collection of points arranged in a specific pattern that is used to define more complex objects such as a wire.
• A plane, on the other hand, is simply a collection of lines in a specific space and direction, similar to land.
  As a result, the three most important undefined terms in geometry are Point, Line, and Plane.

This is accurate since every point on a plane requires an ordered pair of $x$and $y$ coordinates.

Option $\left(E\right)$:

It follows that a plane must consist of an endless number of lines or points, hence this statement is accurate.

The explanation for the incorrect option:

Option $\left(B\right)$:

A point cannot have a dimension, hence the statement is untrue.

Option $\left(C\right)$:

As a one-dimensional entity, a line can only have one dimension, which is its length, hence this assertion is untrue.

Option $\left(D\right)$:

This statement is untrue since a line must have a beginning and an ending point in order for two locations to have a distance between them.

Hence, options $\left(A\right)$ and $\left(E\right)$ are true regarding undefinable terms in geometry.