Step by step
The question
Question: glide reflect the shape A(1, 2), B(4, 2) and C(1, 3): reflect in the x-axis, then translate left 3.
1 Draw the shape
Put the points on the grid and join them.
The mirror line is the x-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 flat.
So the slide goes left or right, along it.
Any other slide is not a glide.
2 Flip
Flip in the x-axis: y changes sign, x stays.
The rule: (x, −y).
A is (1, 2): it goes to (1, −2).
B goes to (4, −2).
C goes to (1, −3).
Join them.
3 Slide
Left 3: x gets 3 smaller.
The rule: (x − 3, y).
A' is (1, −2): it goes to (−2, −2).
B' goes to (1, −2).
C' goes to (−2, −3).
Join them: the final image.
So the image is A''(−2, −2), B''(1, −2) and C''(−2, −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.