Video Transcript
Given a circle with center π
that intersects with line πΏ at points π΄ and π΅, draw an image of circle π
after a reflection in line πΏ. Which of the following
statements is correct? Is it option (A) line segment
π΄π is parallel to line segment π΄π prime? Option (B) line segment π΅π is
parallel to line segment π΅π prime. Option (C) line segment ππ
prime is perpendicular to line segment π΄π΅. Option (D) ππ prime is equal
to π΄π΅. Or option (E) π΄ prime π΅ prime
is greater than π΄π΅.
To reflect a circle in a mirror
line, we must first reflect its center and then preserve its radius. We reflect the center, thatβs
point π, by first creating the perpendicular line to πΏ that passes through
π. Next, we know that line segment
ππ΄ is a radius of our original circle. So, we can trace an arc with
center π΄ and with the same radius. The point where this arc
intersects our line is the center of our image. So, we have the image of our
circle after reflection. We can now use this to identify
the correct statement.
Thereβs no way that π΄π and
π΄π prime can be parallel to one another. They quite clearly meet and
form an acute angle. In fact, π΅π and π΅π prime
cannot be parallel either for the same reasons. Of course, we do know that ππ
prime must be perpendicular to π΄π΅. And this is because we
constructed the perpendicular line bisector of line πΏ at the very start. And line πΏ passes through
π΄π΅. The correct answer is option
(C). Line segment ππ prime is
perpendicular to line segment π΄π΅.