Step by step
The question
Question: glide reflect the shape A(1, −2), B(3, −2) and C(3, 1): translate down 2, 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 2: y gets 2 smaller.
The rule: (x, y − 2).
A is (1, −2): it goes to (1, −4).
B goes to (3, −4).
C goes to (3, −1).
Join them.
3 Flip
Flip in the y-axis: x changes sign, y stays.
The rule: (−x, y).
A' is (1, −4): it goes to (−1, −4).
B' goes to (−3, −4).
C' goes to (−3, −1).
Join them: the final image.
So the image is A''(−1, −4), B''(−3, −4) and C''(−3, −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.