Video Transcript
Which of the following
represents the image of triangle 𝐴𝐵𝐶, where 𝐴 has coordinates one, three; 𝐵
has coordinates three, three; and 𝐶 has coordinates three, seven, after a
transformation 𝑥, 𝑦 is mapped to 𝑥, negative 𝑦? (a) 𝐴 prime negative one,
three; 𝐵 prime negative three, three; and 𝐶 prime negative three, seven. (b) 𝐴 prime negative one,
negative three; 𝐵 prime negative three, negative three; and 𝐶 prime negative
three, negative seven. (c) 𝐴 prime one, negative
three; 𝐵 prime three, negative three; and 𝐶 prime three, negative seven. Or (d) 𝐴 prime three, one; 𝐵
prime three, three; and 𝐶 prime seven, three.
We’re given the rule that
describes this transformation. Every point 𝑥, 𝑦 is mapped to
the point 𝑥, negative 𝑦. In other words, the
𝑥-coordinate stays the same, and the 𝑦-coordinate changes sign or is
multiplied by negative one. We can apply this mapping to
each vertex of triangle 𝐴𝐵𝐶.
The point 𝐴 with coordinates
one, three is mapped to the point 𝐴 prime with coordinates one, negative
three. The point 𝐵 with coordinates
three, three is mapped to three, negative three. And the point 𝐶 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
𝐴𝐵𝐶 on a coordinate grid. If we also plot triangle 𝐴
prime 𝐵 prime 𝐶 prime, we can see that the two triangles appear to be
reflections of one another. The mirror line is the
𝑥-axis. So, this tells us that we can
represent the transformation of reflection in the 𝑥-axis as the mapping 𝑥, 𝑦
is mapped to 𝑥, negative 𝑦, although it’s beyond the current scope to recall
this.
