Video Transcript
Does the given figure allow you to
conclude that the ray starting at 𝐶 and passing through 𝐷 passes through point
𝐵?
In this question, we are given a
figure containing a ray and three points, and we want to use this figure to
determine if a given ray passes through 𝐵. We can begin by recalling that a
ray is a set of all of the points that lie on a line that extends indefinitely in a
single direction. We represent rays using an arrow
above two points. For instance, the ray from 𝑃
through 𝑄 is the set that includes all of the points on the ray that starts at 𝑃
and extends indefinitely in the direction through 𝑄.
If we look at the given diagram, we
can note that the ray in the diagram is the ray starting at 𝐶 that passes through
𝐷. Every point on this line is a point
in the set. The ray extends indefinitely in the
direction that the arrow points. So, if we had a point 𝐸 on the
line in this direction, then we can say that the ray does pass through 𝐸. However, rays only extend
indefinitely in one direction. So, 𝐵 is not on the ray. Hence, the answer is no; the ray
from 𝐶 though 𝐷 does not pass through 𝐵.
