Video Transcript
Which of the following does the
figure illustrate? (A) A bisector of an angle. (B) A straight line parallel to
another line. (C) A perpendicular bisector of a
line segment. (D) A perpendicular to a straight
line originating from it. (E) A perpendicular from a point
lying outside a straight line.
In this question, we have been
given a figure which has been constructed using a ruler and a pair of compasses. We are asked to decide which of
five possible constructions the figure represents. In order to answer this question,
we will begin by demonstrating how the figure can be drawn and then identify the
correct option. Let’s consider how we can construct
this figure given a ruler and pair of compasses.
Consider the line segment 𝐴𝐵 as
shown. We begin by setting the radius of
the compass to be greater than half of 𝐴𝐵 and tracing arcs of a circle centered at
𝐴. We then repeat this with the circle
centered at 𝐵. The arcs intersect at two points
that we will call 𝐶 and 𝐷. Line 𝐶𝐷 is the perpendicular
bisector of line segment 𝐴𝐵 as was demonstrated in the original figure. This means that the answer to this
question is option (C).
It was clear from the original
figure that we have not bisected an angle. Hence, option (A) is not
correct. Likewise, we do not have parallel
lines. So, option (B) is not correct. Whilst options (D) and (E) involve
constructing a perpendicular line, the compass marks would be different here. Hence, we can also rule out options
(D) and (E).
The figure drawn in this question
illustrates a perpendicular bisector of a line segment.
