SME
Grade 10 Math · Problem type
A glide reflection
Use this for “Translate A(1, 2) 5 units right, then reflect it across the x-axis.”
Diagram
Translate 5 right and 0 up, then reflect across the x-axis.
A(1, 2) → A′(6, 2) → A″(6, −2).
Both moves keep lengths and angles, so the final image is congruent to the figure.
This is an example. Type your own values to start a new problem.
A(
x
,
y
)
→
A′(
x′
,
y′
)
→
A″(
x″
,
y″
)
h
Slide right (negative: left)
example
Formulas
x
′
=
x
+
h
6 = 1 + 5
y
′
=
y
2 = 2
x
″
=
x
′
6 = 6
y
″
=
−
y
′
−2 = −2
Assumptions
•
First slide h units right: (x, y) → (x + h, y). Then reflect across the x-axis: (x, y) → (x, −y).
•
A slide along a line followed by a flip in that line is a glide reflection.
Step-by-step
WE KNOW
x = 1, y = 2, h = 5
FIND
x of A′ (x′), y of A′ (y′), x of A″ (x″), y of A″ (y″)
Step 1 · Find x of A′ (x′)
Use x′ = x + h
The
slide
moves
every
point
h
units
across.
x
′
=
1
+
5
x
′
=
6
Step 2 · Find y of A′ (y′)
Use y′ = y
A
slide
across
keeps
y
.
y
′
=
2
Step 3 · Find x of A″ (x″)
Use x″ = x′
Reflecting
across
the
x
-axis
keeps
x
.
x
″
=
6
Step 4 · Find y of A″ (y″)
Use y″ = −y′
Reflecting
across
the
x
-axis
changes
the
sign
of
y
.
y
″
=
−2
Check
Put the numbers back in. Both sides should match.
6 = 1 + 5 ✓
2 = 2 ✓
6 = 6 ✓
−2 = −2 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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Related lessons
Rigid motions, compositions and symmetry
Main lesson
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