### Video Transcript

Which of the following
represents the image of triangle π΄π΅πΆ, where π΄ has coordinates one, three; π΅
has coordinates three, three; and πΆ has coordinates three, seven, after a
transformation π₯, π¦ is mapped to π₯, negative π¦? (a) π΄ prime negative one,
three; π΅ prime negative three, three; and πΆ prime negative three, seven. (b) π΄ prime negative one,
negative three; π΅ prime negative three, negative three; and πΆ prime negative
three, negative seven. (c) π΄ prime one, negative
three; π΅ prime three, negative three; and πΆ prime three, negative seven. Or (d) π΄ prime three, one; π΅
prime three, three; and πΆ prime seven, three.

Weβre given the rule that
describes this transformation. Every point π₯, π¦ is mapped to
the point π₯, negative π¦. In other words, the
π₯-coordinate stays the same, and the π¦-coordinate changes sign or is
multiplied by negative one. We can apply this mapping to
each vertex of triangle π΄π΅πΆ.

The point π΄ with coordinates
one, three is mapped to the point π΄ prime with coordinates one, negative
three. The point π΅ with coordinates
three, three is mapped to three, negative three. And the point πΆ with
coordinates three, seven is mapped to the point three, negative seven. Looking carefully at the four
options given, we can see that this set of coordinates is option (c).

We can also visualize the
effect of this transformation graphically. Here, we have plotted triangle
π΄π΅πΆ on a coordinate grid. If we also plot triangle π΄
prime π΅ prime πΆ prime, we can see that the two triangles appear to be
reflections of one another. The mirror line is the
π₯-axis. So, this tells us that we can
represent the transformation of reflection in the π₯-axis as the mapping π₯, π¦
is mapped to π₯, negative π¦, although itβs beyond the current scope to recall
this.