Video Transcript
Which of the following
constructions represents drawing a perpendicular from a point lying outside a
straight line? We recall that to find a
perpendicular from a point not on a line, we first trace a circle centered at
that point which will intersect the line at the two distinct points. Then, we would trace circles
with the same radius centered on the two points of intersection. These two circles would
intersect at a point which we connect back to the original point, resulting in a
line segment perpendicular to the original line.
Of the five diagrams given, the
only one that matches these construction steps is option (E). First, we notice point 𝐶 is
not on line 𝐴𝐵. We also see a circle centered
on 𝐶 intersecting the line at points 𝐷 and 𝐹. Then, we notice the
intersecting arcs of two circles centered on 𝐷 and 𝐹. This point of intersection then
connects back to point 𝐶, forming a line perpendicular to line 𝐴𝐵.
It is worth noting that the
other options give different geometric constructions. Option (A) is the construction
of a perpendicular bisector. Option (B) finds the
perpendicular to a straight line passing through a point on the line. Option (C) is a bisector;
however, it is not perpendicular. And option (D) is the
construction of an angle bisector.
