Question

which statements are true regarding undefinable terms in geometry? select two options
a points location on the coordinate plane is indicated by an ordered pair, (x, y).
a point has one dimension, length.
a line has length and width.
a distance along a line must have no beginning or end.
a plane consists of an infinite set of points.

Explanation:

• For option A:

In the coordinate plane, by the definition of coordinate system, a point is uniquely determined by an ordered pair \((x,y)\) where \(x\) is the horizontal (abscissa) and \(y\) is the vertical (ordinate) coordinate.

• For option B:

A point is a zero - dimensional object. It has no length, width, or height. So, the statement “A point has one dimension: length” is false.

• For option C:

A line is a one - dimensional object. It has length but no width. So, the statement “A line has length and width” is false.

• For option D:

A distance along a line is a finite quantity (for a line segment) and has a beginning and an end (for a line segment). A line itself (infinite line) is not a distance. So, the statement “A distance along a line must have no beginning or end” is false.

• For option E:

By the definition of a plane in geometry, a plane is a two - dimensional flat surface that extends infinitely in all directions and is composed of an infinite number of points.

Answer:

A. A point's location on the coordinate plane is indicated by an ordered pair, \((x,y)\).
E. A plane consists of an infinite set of points.