Two points

Opposite rays are two rays that both start from a common point and go off in exactly opposite directions. Because of this the two rays (QA and QB in the figure above) form a single straight line through the common endpoint Q. When the two rays are opposite, the points A,Q and B are collinear.

two ways

In geometry, a locus (plural: loci) (Latin word for “place”, “location”) is a set of all points (commonly, a line, a line segment, a curve or a surface), whose location satisfies or is determined by one or more specified conditions.

Collinear Points: points that lie on the same line. Coplanar Points: points that lie in the same plane. Opposite Rays: 2 rays that lie on the same line, with a common endpoint and no other points in common.

A line segment represents a collection of points inside the endpoints and it is named by its endpoints. A ray is a line that only has one defined endpoint and one side that extends endlessly away from the endpoint. A ray is named by its endpoint and by another point on the line.

A ray is a part of a line that has one endpoint and goes on infinitely in only one direction. You cannot measure the length of a ray. A ray is named using its endpoint first, and then any other point on the ray (for example, →BA ).

A ray has one endpoint and goes on forever in one direction. Mathematicians name a ray with notation like , where point E is the endpoint and F is a point on the ray.

No, Ray AB and Ray BA are not same. Ray: It has one initial point and it goes upto infinity. Initial Point of Ray AB is A and that of ray BA is B. So these rays are moving in opposite directions to each other.

The line AB is same as the line BA. A line is a set of points extends in two opposite directions without end.

Definition: A vector is just a direction. To get a vector, subtract two points from each other. If you have points A and B, then the vector AB is B-A. The vector BA is A-B.

If A and B are n×n matrices, then both AB and BA are well defined n×n matrices. However, in general, AB = BA. If AB does equal BA, we say that the matrices A and B commute.

Why do you use two arrowheads when drawing or naming a line? It continues on in both directions infinitely. A ray goes on infinitely in one direction, whereas a line goes on infinitely in both directions.

Answer: Two other ways to name EF are EBF and FBE.

There is exactly one plane containing a given line and point not on the line.

Through any three points, there is exactly one plane. SOLUTION: If the points were non-collinear, there would be exactly one plane by Postulate 2.2 shown by Figure 1. If the points were collinear, there would be infinitely many planes. Figure 2 shows what two planes through collinear points would look like.

Three non-collinear points determine a plane. This statement means that if you have three points not on one line, then only one specific plane can go through those points. The plane is determined by the three points because the points show you exactly where the plane is.

Collinear Points Do Not Determine a Plane Three points must be noncollinear to determine a plane. Here, these three points are collinear. Notice that at least two planes are determined by these collinear points. Actually, these collinear points determine an infinite number of planes.