Rays - Concept


A ray is part of a line, has one fixed endpoint, and extends infinitely along the line from the endpoint. Opposite math rays are rays with a common endpoint, extending in opposite directions and forming a line.


If we had a line so it extends infinitely
in either direction, and I picked
an end point somewhere, and I erased everything
that extended beyond that
end point, what I've just
created is a ray.
So a ray has one end point and it extends
infinitely from that end point.

But how do you label a ray?
Well, you start off by saying
what is your end point?
My end point of this ray is A because that's
where it starts, and it extends
through point B. So I'm going to
label this ray A, B as a line but
I only have one arrow.
So the arrow is going
to be over the B.
Because my end point is A and notice I
do not have an arrow over the A, which
tells the geometry student or the geometry
teacher that this ray starts
at A and passes through B.

Now, you can also have opposite rays,
and opposite rays share
a common end point.
So if you look at this line right here,
containing X, Y and Z where X, Y and
Z are all co-linear.
We have opposite rays
if I pick point Y.
So I could say that the ray Y, Z -- so
again I'm saying from point Y through
point Z. So go YZ, and notice how
I level this where the arrow is
over the Z because it starts at Y and
the opposite one would be the ray
starting at Y passing
through X.
So I could label this as ray YX.

So opposite rays share an end point and
rays in general have one end point and
extend infinitely from
that end point.

ray line endpoint opposite rays