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