SME
Grade 8 Math · Geometry
Translations, rotations, reflections and dilations
Use this for “Translate (−6, 2) right 7 and down 4. Where is its image?”
Diagram
Translate 7 right and 4 down: (x, y) → (x + 7, y − 4).
A(−6, 2) → A′(1, −2); B′(5, −2), C′(2, 1).
The image has the same side lengths and angles.
This is an example. Type your own values to start a new problem.
(
x
+
h
,
y
+
(
k
)
)
=
(
x′
,
y′
)
Formulas
x
′
=
x
+
h
(x
of
A′
=
x
of
A
+
right)
1 = −6 + 7
y
′
=
y
+
k
(y
of
A′
=
y
of
A
+
up)
−2 = 2 + (−4)
Assumptions
•
A translation slides every point the same distance the same way.
•
h is the slide right (left when negative), k the slide up (down when negative).
•
Lengths and angles do not change: the image is congruent.
•
Drag A′ to change the slide.
Step-by-step
WE KNOW
x = −6 (x of A), y = 2 (y of A), h = 7 (right), k = −4 (up)
FIND
x of A′ (x′), y of A′ (y′)
Step 1 · Find x of A′ (x′)
Use x′ = x + h (x of A′ = x of A + right)
Slide
A
across
by
h
.
x
′
=
−6
+
7
x
′
=
1
Step 2 · Find y of A′ (y′)
Use y′ = y + k (y of A′ = y of A + up)
Slide
A
up
by
k
.
y
′
=
2
+
(−4)
y
′
=
−2
Check
Put the numbers back in. Both sides should match.
1 = −6 + 7 ✓
−2 = 2 + (−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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More problem types
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