SME
Grade 10 Math · Problem type
Reflecting across y = x or y = −x
Use this for “Reflect A(4, 1) across the line y = x” or “across y = −x.”
Diagram
Reflect across y = −x: (x, y) → (−y, −x).
A(4, 1) → A′(−1, −4); B′(−4, −4), C′(−4, −2).
The image has the same side lengths and angles.
This is an example. Type your own values to start a new problem.
A(
x
,
y
)
→
A′(
x′
,
y′
)
s
Mirror line
example
Formulas
x
′
=
s
×
y
−1
=
y
=
−
x
×
1
y
′
=
s
×
x
−4
=
y
=
−
x
×
4
Assumptions
•
Across y = x the coordinates swap: (x, y) → (y, x).
•
Across y = −x they swap and both signs change: (x, y) → (−y, −x).
•
Each point and its image are the same distance from the line, on a segment at right angles to it.
Step-by-step
WE KNOW
x = 4, y = 1, s: y = −x
FIND
x of A′ (x′), y of A′ (y′)
Step 1 · Find x of A′ (x′)
Use x′ = s × y
Across
y
=
−
x
,
the
new
x
is
the
old
y
with
its
sign
changed.
x
′
=
−
y
x
′
=
−1
Step 2 · Find y of A′ (y′)
Use y′ = s × x
Across
y
=
−
x
,
the
new
y
is
the
old
x
with
its
sign
changed.
y
′
=
−
x
y
′
=
−4
Check
Put the numbers back in. Both sides should match.
−1 = −1 ✓
−4 = −4 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
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Rigid motions, compositions and symmetry
Main lesson
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