Video Transcript
Which of the following is
equivalent to a translation of 𝑥, 𝑦 is mapped to 𝑥 plus two, 𝑦 minus three? (A) A translation of two units
right and three units up. (B) A translation of two units left
and three units down. (C) A translation of two units
right and three units down. (D) A translation of three units
right and two units up. Or (E) a translation of three units
right and two units down.
We’ve been given this translation
in the form of a mapping, and we want to determine what it means in words. We can recall that, in general, the
translation represented by the mapping 𝑥, 𝑦 is mapped to 𝑥 plus 𝑎, 𝑦 plus 𝑏
has a horizontal displacement of 𝑎 units and a vertical displacement of 𝑏
units. The signs of 𝑎 and 𝑏 tell us the
direction in which the translation occurs.
Looking at the mapping here, the
value of 𝑎 is positive two and the value of 𝑏 is negative three. So the horizontal displacement is
positive two, which means two units to the right. The vertical displacement is
negative three. And as we are subtracting three
from the 𝑦-coordinate, this means three units down. Looking carefully at the five
options we were given, we can see that a translation of two units right and three
units down is option (C).
