Step by step
The question
Question: glide reflect the shape A(−2, −1), B(0, −1) and C(−2, −3): translate right 3, 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 3: x gets 3 bigger.
The rule: (x + 3, y).
A is (−2, −1): it goes to (1, −1).
B goes to (3, −1).
C goes to (1, −3).
Join them.
3 Flip
Flip in the x-axis: y changes sign, x stays.
The rule: (x, −y).
A' is (1, −1): it goes to (1, 1).
B' goes to (3, 1).
C' goes to (1, 3).
Join them: the final image.
So the image is A''(1, 1), B''(3, 1) and C''(1, 3).
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.