Video Transcript
How can the line shown in the
figure be represented mathematically? Option (A) 𝐴𝐵. Option (B) the ray from 𝐴
through 𝐵. Option (C) the ray from 𝐵
through 𝐴. Option (D) the line through 𝐴
and 𝐵. Or is it option (E) the line
segment 𝐴𝐵?
In this question, we are given
a line and two points on this line. And we are asked to represent
the figure mathematically.
To do this, we first note that
there are arrows on both sides of the line. So this line extends
indefinitely in both directions. We can also note that we have
two distinct points 𝐴 and 𝐵 that lie on the line. We can then recall that we can
represent that a line extends indefinitely in both directions by using a
double-sided arrow above two distinct points which lie on the line. This gives us two different
equivalent ways of representing this line. We can see that this only
matches option (D).
We can also check what is
represented by the four other options. First, we recall that 𝐴𝐵
without any further notation means the length of the line segment between these
two points. Second, we recall that a
one-sided arrow represents a ray, that is, a straight line that extends
indefinitely in a single direction. The first point is the initial
point of the ray. We know that the given figure
is not a ray, since it extends indefinitely in both directions.
Finally, we recall that a line
above the points represents a line segment, that is, the finite line segment
between the two points. This is not the same as the
given line, since the figure extends indefinitely in both directions. Hence, the answer is option
(D).
