Video Transcript
Which of the following represents
the image of triangle 𝐴𝐵𝐶, where 𝐴 has coordinates one, two; 𝐵 has coordinates
one, five; and 𝐶 has coordinates three, five, after a transformation that maps 𝑥,
𝑦 onto 𝑥 plus three, 𝑦 minus two? Option (A) 𝐴 prime four, two; 𝐵
prime four, five; and 𝐶 prime six, five. Option (B) 𝐴 prime one, zero; 𝐵
prime one, three; and 𝐶 prime three, three. Option (C) 𝐴 prime four, zero; 𝐵
prime four, three; and 𝐶 prime six, three. Or option (D) 𝐴 prime negative
one, five; 𝐵 prime negative one, eight; and 𝐶 prime one, eight.
We’re given the rule that describes
this transformation. Every point 𝑥, 𝑦 is mapped to the
point 𝑥 plus three, 𝑦 minus two. We note that this transformation is
a translation. A translation of an object is when
the object is moved by sliding it by a set number of units vertically and
horizontally. According to the given rule, the
triangle will be translated three units to the right and two units down.
To find out which of the options
given represents the image of triangle 𝐴𝐵𝐶, we substitute the coordinates of each
of the vertices of triangle 𝐴𝐵𝐶 into the translation rule to give us the vertices
of the image. The point 𝐴 with coordinates one,
two is mapped to the point 𝐴 prime. The coordinates of 𝐴 prime are
found by adding three to the 𝑥-coordinate one and subtracting two from the
𝑦-coordinate two. So, 𝐴 prime has coordinates four,
zero. According to the same rule, point
𝐵 with coordinates one, five is mapped to the point 𝐵 prime with coordinates four,
three. And finally, the point 𝐶 with
coordinates three, five is mapped to point 𝐶 prime with coordinates six, three, as
shown.
Looking carefully at the four
options given, we can see that this set of coordinates is option (C). In conclusion, we found the
coordinates of the image of triangle 𝐴𝐵𝐶 by applying the translation rule to each
vertex.
