Step by step
The question
Question: glide reflect the shape A(2, −1), B(4, −1) and C(2, −3): translate left 2, then reflect in the line y = −2.
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 Slide
Left 2: x gets 2 smaller.
The rule: (x − 2, y).
A is (2, −1): it goes to (0, −1).
B goes to (2, −1).
C goes to (0, −3).
Join them.
3 Flip
Flip in the line y = −2: count from the point to the line, then the same again on the other side.
A' is (0, −1): it goes to (0, −3).
B' goes to (2, −3).
C' goes to (0, −1).
Join them: the final image.
So the image is A''(0, −3), B''(2, −3) and C''(0, −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.