Begin by undoing the reflection that creates â–ł A''B''C''.
Translation: (x,y)→ (x+3,y+3)
Practice makes perfect
From the exercise we know that â–ł A''B''C'' is created by reflecting its preimage, â–ł A'B'C', in the line of reflection y=x. Let's undo this reflection so that we can compare â–ł A'B'C' with â–ł ABC, the two triangles where the translation takes place.
Now we can compare corresponding vertices of â–ł A'B'C' and â–ł ABC to determine the translation. Note that the line of reflection, y=x, is parallel to the direction of the translation. This is a criteria for a transformation to be classified as a glide reflection.
Recall that the horizontal translation affects the x-coordinate, and that the vertical translation affects the y-coordinate. With the information provided above, we can write the rule for the translation of the glide reflection.
(x,y)→ (x+ 3,y+3)
