Step by step
The question
Question: glide reflect the shape A(2, 1), B(3, 3) and C(4, 1): reflect in the line y = −1, then translate left 4.
1 Draw the shape
Put the points on the grid and join them.
The mirror line is the line y = −1.
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 = −1: count from the point to the line, then the same again on the other side.
A is (2, 1): it goes to (2, −3).
B goes to (3, −5).
C goes to (4, −3).
Join them.
3 Slide
Left 4: x gets 4 smaller.
The rule: (x − 4, y).
A' is (2, −3): it goes to (−2, −3).
B' goes to (−1, −5).
C' goes to (0, −3).
Join them: the final image.
So the image is A''(−2, −3), B''(−1, −5) and C''(0, −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.