Begin by undoing the reflection that creates â–³ A''B''C''.
Translation: (x,y)→ (x+3,y+3)
Practice makes perfect
From the exercise we know that â–³ A''B''C'' is created by reflecting its preimage, â–³ A'B'C', in the line of reflection y=x. Let's undo this reflection so that we can compare â–³ A'B'C' with â–³ ABC, the two triangles where the translation takes place.
Now we can compare corresponding vertices of â–³ A'B'C' and â–³ 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)
