Step by step
The question
Question: glide reflect the shape A(1, 2), B(3, 2) and C(1, 4): translate right 4, then reflect in the x-axis.
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 Slide
Right 4: x gets 4 bigger.
The rule: (x + 4, y).
A is (1, 2): it goes to (5, 2).
B goes to (7, 2).
C goes to (5, 4).
Join them.
3 Flip
Flip in the x-axis: y changes sign, x stays.
The rule: (x, −y).
A' is (5, 2): it goes to (5, −2).
B' goes to (7, −2).
C' goes to (5, −4).
Join them: the final image.
So the image is A''(5, −2), B''(7, −2) and C''(5, −4).
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.