SME
Grade 8 Math · Problem type
Reflection over a horizontal line
Use this for “(3, 7) is reflected over the x-axis. Where is its image?”
Diagram
Reflect across y = 0: (x, y) → (x, −y).
A(3, 7) → A′(3, −7); B′(6, −2), C′(2, −2).
The image has the same side lengths and angles.
This is an example. Type your own values to start a new problem.
x
x of A
example
y
y of A
example
a
Mirror line’s y
example
x′
x of A′
calculated
y′
y of A′
calculated
Formulas
x
′
=
x
(x
of
A′
=
x
of
A)
3 = 3
y
′
=
2
×
a
−
y
(y
of
A′
=
2
×
mirror
line’s
y
−
y
of
A)
−7 = 2 × 0 − 7
Assumptions
•
The mirror is the horizontal line y = a (the x-axis is a = 0).
•
Each corner and its image are the same distance above and below the line.
•
Over the x-axis, y changes sign and x stays the same.
Step-by-step
WE KNOW
x = 3 (x of A), y = 7 (y of A), a = 0 (mirror line’s y)
FIND
x of A′ (x′), y of A′ (y′)
Step 1 · Find x of A′ (x′)
Use x′ = x (x of A′ = x of A)
A
flip
over
a
horizontal
line
keeps
x
.
x
′
=
3
Step 2 · Find y of A′ (y′)
Use y′ = 2 × a − y (y of A′ = 2 × mirror line’s y − y of A)
As far below the line as A is above it.
y
′
=
2
×
0
−
7
y
′
=
0
−
7
y
′
=
−7
Check
Put the numbers back in. Both sides should match.
3 = 3 ✓
−7 = 2 × 0 − 7 ✓
Topic check
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Related lessons
Translations, rotations, reflections and dilations
Main lesson
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