Points, Lines, and Planes

Line

A line is a straight collection of an infinite number of points. Infinite numbers of lines can be draw through one point, but only one line can be drawn connecting two lines. You cannot draw one straight line through three or more points if they do not have the same x or y value. It takes two distinct points to determine a line. There are two ways to name a line: 1) Take two chronological numbers from the line and draw a line with arrows on both ends to indicate that is continues infinity in two directions. A line can also be represented as a lower case italicized letter.

Line Segment

A line segment is the part of a line consisting of two endpoints and all points between them. A line segment is usually called just segment and is named by its two endpoints. It is written with a bar over the letters, with no arrows on the bar.

Intersecting

A line that divides another by passing through it.

Plane

A plane is a flat surface that extends infinitely in all directions. It is made up of at least three noncollinear points. A plane is labeled by an uppercase script letter or by using points that are on the plane. Just like two points determine a line, three noncollinear points determine a unique plane.

How do we name a plane?

A plane is labeled by an uppercase script letter or by using points that are on the plane.

Do points have a measurable dimension?

A point is a fixed location in a space; it has no dimension. A pint is represented as a dot, but it actually has no length, width, or thickness.

Point

A point is a fixed location in a space; it has no dimension. A pint is represented as a dot, but it actually has no length, width, or thickness. A point is named using a capital letter. The points X, P, N, and R represent different points because the represent different locations. The location of a pin can be written in (x,y) format.

How do we name a point?

A point is named using a capital letter. The points X, P, N, and R represent different points because the represent different locations. The location of a pin can be written in (x,y) format.

What is the intersection of two planes?

A single point.

What is the intersection of two lines?

An intersection.

Co-planar

Co-planar are points or lines that lie on the same plane.

How many lines can be drawn through one point?

Infinite numbers of lines can be draw through one point, but only one line can be drawn connecting two lines.

How many points determine a plane?

It is made up of at least three noncollinear points.

How do we name a line segment?

It is written with a bar over the letters, with no arrows on the bar.

How many points determine a line?

It takes two distinct points to determine a line.

Skew Lines

Lines that are not co-planar and line that do not intersect are called skew lines.

Non-Coplanar

Non co-planar lines are points or lines that do not lie on the same plane.

Parallel Lines

Parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel.

How do we name a line?

There are two ways to name a line. Take two chronological numbers from the line and draw a line with arrows on both ends to indicate that is continues infinity in two directions. A line can also be represented as a lower case italicized letter.

Collinear

Three or more points that lie on the same line are called collinear. Three or more points that do not lie on the same line are noncollinear.