### Video Transcript

Victoria reflected point 𝑃 and
point 𝑄 across one of the dotted lines in the grid. Complete the following. She reflected point 𝑃 across line
blank and point 𝑄 across line blank.

We’ve been told that Victoria
reflected two points 𝑃 and 𝑄 across one of the dotted lines in the grid. And we need to determine which line
she reflected each point across. We can see points 𝑃 and 𝑄 on the
grid as well as their images 𝑃 prime and 𝑄 prime after their reflections. The two possible mirror lines are
labeled line 𝐿 and line 𝑀.

To answer this question, we need to
recall that a reflection preserves the perpendicular distance of a point from the
mirror line. Each of the mirror lines on the
grid are vertical. So the perpendicular distance of
each point from either mirror line will be horizontal. If we connect points 𝑃 and 𝑃
prime, then the mirror line must intersect this line segment at its midpoint so that
points 𝑃 and 𝑃 prime are the same perpendicular distance from the mirror line. In fact, the mirror line will be
the perpendicular bisector of the line segment 𝑃𝑃 prime.

If we consider line 𝑀, we can see
that point 𝑃 is four squares away horizontally, whereas 𝑃 prime is two squares
away horizontally. Therefore, line 𝑀 cannot be the
mirror line used for point 𝑃 as the perpendicular distances are different. If, however, we consider the
perpendicular distance between line 𝐿 and the points 𝑃 and 𝑃 prime, we can see
that in each case this perpendicular distance is three squares. So this tells us that Victoria
reflected point 𝑃 across line 𝐿.

Next, we consider point 𝑄. And we can draw in the line segment
connecting 𝑄 and 𝑄 prime. This time, we can see that line 𝑀
passes through the midpoint of this line segment and that points 𝑄 and 𝑄 prime are
each two squares horizontally away from line 𝑀. So, for point 𝑄, the mirror line
was line 𝑀.

By considering the perpendicular
distance of each point and its image from the possible mirror lines, we’ve found
that Victoria reflected point 𝑃 across line 𝐿 and point 𝑄 across line 𝑀.