Worked examples
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.
A(1, 2), B(3, 2) and C(1, 4)
= slide right 4, flip in 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.
glide reflection = slide along the mirror line + flip
Careful!
The mirror line is flat.
So the slide goes left or right, along it.
Any other slide is not a glide.
Careful: the slide goes along the mirror line: left or right
2 Slide
Right 4: x gets 4 bigger.
The rule: (x + 4, y).
slide right 4: (x, y) → (x + 4, y)
A is (1, 2): it goes to (5, 2).
A(1, 2) → A'(5, 2)
B goes to (7, 2).
B(3, 2) → B'(7, 2)
C goes to (5, 4).
C(1, 4) → C'(5, 4)
Join them.
3 Flip
Flip in the x-axis: y changes sign, x stays.
The rule: (x, −y).
flip in x-axis: (x, y) → (x, −y)
A' is (5, 2): it goes to (5, −2).
A'(5, 2) → A''(5, −2)
B' goes to (7, −2).
B'(7, 2) → B''(7, −2)
C' goes to (5, −4).
C'(5, 4) → C''(5, −4)
Join them: the final image.
So the image is A''(5, −2), B''(7, −2) and C''(5, −4).
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.
flip first, then slide:
A(1, 2) → (1, −2) → (5, −2)
B(3, 2) → (3, −2) → (7, −2)
The same points as before.
Right!
C(1, 4) → (1, −4) → (5, −4)
Let's look back.
First: draw the shape.
Then: slide.
Then: flip.
Last: check.
Answer A''(5, −2), B''(7, −2) and C''(5, −4)
▶ Watch it solved
The question
Question: glide reflect the shape A(1, 3), B(3, 3) and C(1, 5): translate right 3, then reflect in the line y = 1.
A(1, 3), B(3, 3) and C(1, 5)
= slide right 3, flip in 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.
glide reflection = slide along the mirror line + flip
Careful!
The mirror line is flat.
So the slide goes left or right, along it.
Any other slide is not a glide.
Careful: the slide goes along the mirror line: left or right
2 Slide
Right 3: x gets 3 bigger.
The rule: (x + 3, y).
slide right 3: (x, y) → (x + 3, y)
A is (1, 3): it goes to (4, 3).
A(1, 3) → A'(4, 3)
B goes to (6, 3).
B(3, 3) → B'(6, 3)
C goes to (4, 5).
C(1, 5) → C'(4, 5)
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.
flip in line y = 1: count to the line, the same again
A' is (4, 3): it goes to (4, −1).
A'(4, 3) → A''(4, −1)
B' goes to (6, −1).
B'(6, 3) → B''(6, −1)
C' goes to (4, −3).
C'(4, 5) → C''(4, −3)
Join them: the final image.
So the image is A''(4, −1), B''(6, −1) and C''(4, −3).
A''(4, −1), B''(6, −1) and C''(4, −3)
4 Check
Let's check the other way round: flip first, then slide.
For a glide, it must give the same points.
flip first, then slide:
A(1, 3) → (1, −1) → (4, −1)
B(3, 3) → (3, −1) → (6, −1)
The same points as before.
Right!
C(1, 5) → (1, −3) → (4, −3)
Let's look back.
First: draw the shape.
Then: slide.
Then: flip.
Last: check.
Answer A''(4, −1), B''(6, −1) and C''(4, −3)
▶ Watch it solved
The question
Question: glide reflect the shape A(−3, 1), B(−1, 1) and C(−1, 3): reflect in the line x = 1, then translate down 2.
A(−3, 1), B(−1, 1) and C(−1, 3)
= slide down 2, flip in line x = 1
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.
glide reflection = slide along the mirror line + flip
Careful!
The mirror line is upright.
So the slide goes up or down, along it.
Any other slide is not a glide.
Careful: the slide goes along the mirror line: up or down
2 Flip
Flip in the line x = 1: count from the point to the line, then the same again on the other side.
flip in line x = 1: count to the line, the same again
A is (−3, 1): it goes to (5, 1).
A(−3, 1) → A'(5, 1)
B goes to (3, 1).
B(−1, 1) → B'(3, 1)
C goes to (3, 3).
C(−1, 3) → C'(3, 3)
Join them.
3 Slide
Down 2: y gets 2 smaller.
The rule: (x, y − 2).
slide down 2: (x, y) → (x, y − 2)
A' is (5, 1): it goes to (5, −1).
A'(5, 1) → A''(5, −1)
B' goes to (3, −1).
B'(3, 1) → B''(3, −1)
C' goes to (3, 1).
C'(3, 3) → C''(3, 1)
Join them: the final image.
So the image is A''(5, −1), B''(3, −1) and C''(3, 1).
A''(5, −1), B''(3, −1) and C''(3, 1)
4 Check
Let's check the other way round: slide first, then flip.
For a glide, it must give the same points.
slide first, then flip:
A(−3, 1) → (−3, −1) → (5, −1)
B(−1, 1) → (−1, −1) → (3, −1)
The same points as before.
Right!
C(−1, 3) → (−1, 1) → (3, 1)
Let's look back.
First: draw the shape.
Then: flip.
Then: slide.
Last: check.
Answer A''(5, −1), B''(3, −1) and C''(3, 1)
▶ Watch it solved
