Step by step
The question
Question: glide reflect the shape A(−3, 1), B(−1, 1) and C(−1, 2): translate down 3, then reflect in the y-axis.
1 Draw the shape
Put the points on the grid and join them.
The mirror line is the y-axis.
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 upright.
So the slide goes up or down, along it.
Any other slide is not a glide.
2 Slide
Down 3: y gets 3 smaller.
The rule: (x, y − 3).
A is (−3, 1): it goes to (−3, −2).
B goes to (−1, −2).
C goes to (−1, −1).
Join them.
3 Flip
Flip in the y-axis: x changes sign, y stays.
The rule: (−x, y).
A' is (−3, −2): it goes to (3, −2).
B' goes to (1, −2).
C' goes to (1, −1).
Join them: the final image.
So the image is A''(3, −2), B''(1, −2) and C''(1, −1).
4 Check
Let's check the other way round: flip first, then slide.
For a glide, it must give the same points.
The same points as before.
Right!
Let's look back.
First: draw the shape.
Then: slide.
Then: flip.
Last: check.