Video Transcript
The given figure shows a
triangle on the coordinate plane. Sketch the image of the
triangle after the geometric transformation 𝑥, 𝑦 is mapped to negative 𝑦,
𝑥.
We are told that the geometric
transformation we need to apply is at a general point with coordinates 𝑥, 𝑦 is
mapped to the point with coordinates negative 𝑦, 𝑥. This means that the 𝑥- and
𝑦-coordinates swap around, and then we also change the sign of the new
𝑥-coordinate. We can apply this mapping to
the coordinates of each vertex of triangle 𝐴𝐵𝐶 individually.
The coordinates of vertex 𝐴
are two, four. Applying the given mapping, so
swapping the coordinates around and then changing the sign of the new
𝑥-coordinate, gives the point 𝐴 prime with coordinates negative four, two. We can plot this point on the
coordinate grid to show the image of point 𝐴. The coordinates of point 𝐵 are
three, one. Applying the given mapping
gives the coordinates of 𝐵 prime as negative one, three, and then we can also
plot this point. Finally, the coordinates of
point 𝐶 are one, one, which under the given transformation is mapped to
negative one, one. Plotting point 𝐶 prime and
then connecting the three points together gives the image of triangle 𝐴𝐵𝐶
after the given transformation.
Although it isn’t required, we
can also observe that the type of transformation that has been applied is a
rotation, because the orientation of the triangle has changed: it’s now on its
side compared to its original orientation.
