Step by step
The question
Question: glide reflect the shape A(1, 1), B(1, 3) and C(2, 1): reflect in the line x = −1, then translate up 2.
1 Draw the shape
Put the points on the grid and join them.
The mirror line is the line x = −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 upright.
So the slide goes up or down, along it.
Any other slide is not a glide.
2 Flip
Flip in the line x = −1: count from the point to the line, then the same again on the other side.
A is (1, 1): it goes to (−3, 1).
B goes to (−3, 3).
C goes to (−4, 1).
Join them.
3 Slide
Up 2: y gets 2 bigger.
The rule: (x, y + 2).
A' is (−3, 1): it goes to (−3, 3).
B' goes to (−3, 5).
C' goes to (−4, 3).
Join them: the final image.
So the image is A''(−3, 3), B''(−3, 5) and C''(−4, 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.