Video Transcript
The vertices of a square are
transformed by the transformation 𝑥, 𝑦 is mapped to negative 𝑥, 𝑦. Which of the following
geometric transformations is performed? (a) Translation, (b) rotation,
or (c) reflection.
We’re told that the vertices of
this square are transformed by the transformation 𝑥, 𝑦 is mapped to negative
𝑥, 𝑦. So, for each vertex, the
𝑥-coordinate changes sign, and the 𝑦-coordinate stays the same. We’re not given the coordinates
of the vertices of this square. So we may find it helpful to
choose some arbitrary coordinates ourselves to help with visualizing the
transformation. Let’s choose the points one,
one; one, two; two, two; and two, one to be the coordinates of 𝐴, 𝐵, 𝐶, and
𝐷, respectively.
Under the given transformation,
point 𝐴 will be mapped to the point 𝐴 prime with coordinates negative one,
one. And we can add the image of
point 𝐴 to the coordinate grid. Point 𝐵 with coordinates one,
two will be mapped to negative one, two. Point 𝐶 will be mapped to
negative two, two. And point 𝐷 will be mapped to
negative two, one.
Now we need to compare the two
shapes to determine the type of transformation that has occurred. We can see that the square has
been flipped over. For example, the vertices 𝐴
and 𝐵 are originally on the left of the square, and in its image, they are on
the right. The type of transformation is
therefore a reflection. Whilst it’s not required, we
can also identify that the position of the mirror line is along the 𝑦-axis. So the answer is option (c), a
reflection.
