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