Video Transcript
The given figure shows a triangle
on the coordinate plane. Sketch the image of the triangle
after the geometric transformation that maps 𝑥, 𝑦 onto 𝑥 plus three, 𝑦 minus
one. Which of the following matches your
sketch?
Looking at the given figure, we can
see that the vertices of the triangle are 𝐴 with coordinates two, four; 𝐵 with
coordinates three, zero; and 𝐶 with coordinates zero, zero. Having found the vertices, we can
then apply the rule for the geometric transformation that maps 𝑥, 𝑦 onto 𝑥 plus
three, 𝑦 minus one to each set of coordinates to find the coordinates of the
image. The image will have vertices 𝐴
prime, 𝐵 prime, and 𝐶 prime.
For point 𝐴, we use 𝑥 equal to
two and 𝑦 equal to four, since they are the 𝑥-coordinate and the 𝑦-coordinate for
𝐴. By Substituting this into the rule,
we get 𝐴 prime with coordinates five, three. For point 𝐵, we use 𝑥 equal to
three and 𝑦 equal to zero. Substituting this into the rule
then gives us the coordinates of 𝐵 prime, which are six, negative one. And finally, for point 𝐶, we use
𝑥 equal to zero and 𝑦 equal to zero. Substituting this into the rule
gives us the coordinates of 𝐶 prime: three, negative one.
Now that we have found the
coordinates of the vertices of the image, we can plot them on the coordinate
plane. Doing so gives us the
following. Lastly, we join up the vertices
with edges to obtain a sketch of the image, triangle 𝐴 prime 𝐵 prime 𝐶 prime. Comparing this with our options, we
can see that this is the same as the sketch in option (c). We note that the transformation of
triangle 𝐴𝐵𝐶 is a translation, specifically horizontally three units to the right
and vertically one unit down.
