Step by step
The question
Question: glide reflect the shape A(−1, −1), B(1, −1) and C(1, 1): reflect in the line y = 2, then translate right 3.
1 Draw the shape
Put the points on the grid and join them.
The mirror line is the line y = 2.
A glide reflection is a slide along the mirror line, and a flip in it.
Like footprints in the sand: left, right, left.
Careful!
The mirror line is flat.
So the slide goes left or right, along it.
Any other slide is not a glide.
2 Flip
Flip in the line y = 2: count from the point to the line, then the same again on the other side.
A is (−1, −1): it goes to (−1, 5).
B goes to (1, 5).
C goes to (1, 3).
Join them.
3 Slide
Right 3: x gets 3 bigger.
The rule: (x + 3, y).
A' is (−1, 5): it goes to (2, 5).
B' goes to (4, 5).
C' goes to (4, 3).
Join them: the final image.
So the image is A''(2, 5), B''(4, 5) and C''(4, 3).
4 Check
Let's check the other way round: slide first, then flip.
For a glide, it must give the same points.
The same points as before.
Right!
Let's look back.
First: draw the shape.
Then: flip.
Then: slide.
Last: check.