Video Transcript
Find the coordinates of the image
of the point 13, four under the translation 𝑥, 𝑦 is mapped to 𝑥 plus five, 𝑦
minus two.
We’ve been given this
transformation algebraically. We can recall that the given
mapping notation means that this translation has a horizontal displacement of five
units and a vertical displacement of negative two units. In other words, the translation
maps each point five units to the right and two units down. It’s two units down because we are
subtracting two from the 𝑦-coordinate.
Applying this mapping to the point
with coordinates 13, four gives the point with coordinates 13 plus five, four minus
two, which is the point with coordinates 18, two. We could also apply this
transformation graphically if we had access to squared paper on which to draw a
coordinate grid. Here’s the point with coordinates
13, four. To add five to the 𝑥-coordinate,
we move five units to the right. And then to subtract two from the
𝑦-coordinate, we move two units down. The image of the point 13, four
following this translation is indeed the point with coordinates 18, two.
