SME
Grade 8 Math · Problem type
Reflection
Use this for “(3, 7) is reflected over the y-axis. Where is its image?”
Diagram
Reflect across x = 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 x
example
x′
x of A′
calculated
y′
y of A′
calculated
Formulas
x
′
=
2
×
a
−
x
(x
of
A′
=
2
×
mirror
line’s
x
−
x
of
A)
−3 = 2 × 0 − 3
y
′
=
y
(y
of
A′
=
y
of
A)
7 = 7
Assumptions
•
A reflection flips the figure over the mirror line x = a (the y-axis is a = 0).
•
Each corner and its image are the same distance from the line.
•
Over the y-axis, x changes sign; over the x-axis, y would change sign instead.
Step-by-step
WE KNOW
x = 3 (x of A), y = 7 (y of A), a = 0 (mirror line’s x)
FIND
x of A′ (x′), y of A′ (y′)
Step 1 · Find x of A′ (x′)
Use x′ = 2 × a − x (x of A′ = 2 × mirror line’s x − x of A)
As far past the line as A is before it.
x
′
=
2
×
0
−
3
x
′
=
0
−
3
x
′
=
−3
Step 2 · Find y of A′ (y′)
Use y′ = y (y of A′ = y of A)
A
flip
over
a
vertical
line
keeps
y
.
y
′
=
7
Check
Put the numbers back in. Both sides should match.
−3 = 2 × 0 − 3 ✓
7 = 7 ✓
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Reflection over a horizontal line
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Related lessons
Translations, rotations, reflections and dilations
Main lesson
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