SME
Grade 8 Math · Problem type
Dilation
Use this for “Dilate (1, 1) from the origin by a scale factor of 3.”
Diagram
Dilate by scale factor 3 from (0, 0): (x, y) → (3x, 3y).
A(1, 1) → A′(3, 3); B′(9, 3), C′(3, 6).
Each side is 3 times as long; the angles stay the same.
This is an example. Type your own values to start a new problem.
(
k
×
x
,
k
×
y
)
=
(
x′
,
y′
)
Formulas
x
′
=
k
×
x
(x
of
A′
=
scale
factor
×
x
of
A)
3 = 3 × 1
y
′
=
k
×
y
(y
of
A′
=
scale
factor
×
y
of
A)
3 = 3 × 1
Assumptions
•
A dilation from (0, 0) multiplies every coordinate by the scale factor k.
•
A factor above 1 enlarges the figure; between 0 and 1 it shrinks it.
•
The image is similar: the same angles, every length k times as long.
Step-by-step
WE KNOW
x = 1 (x of A), y = 1 (y of A), k = 3 (scale factor)
FIND
x of A′ (x′), y of A′ (y′)
Step 1 · Find x of A′ (x′)
Use x′ = k × x (x of A′ = scale factor × x of A)
Multiply
x
by
the
scale
factor.
x
′
=
3
×
1
x
′
=
3
Step 2 · Find y of A′ (y′)
Use y′ = k × y (y of A′ = scale factor × y of A)
Multiply
y
by
the
scale
factor.
y
′
=
3
×
1
y
′
=
3
Check
Put the numbers back in. Both sides should match.
3 = 3 × 1 ✓
3 = 3 × 1 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Refresh
Related lessons
Translations, rotations, reflections and dilations
Main lesson
Reflection
Use this for “(3, 7) is reflected over the y-axis. Where is its image?”
Reflection over a horizontal line
Use this for “(3, 7) is reflected over the x-axis. Where is its image?”
Rotation about the origin
Use this for “Rotate (3, 1) by 90° counterclockwise about (0, 0).”
Similar triangles
Use this for “Two triangles are similar. One has sides 8, 12 and x; the matching sides of the other are 6, y and 12. Find x and y.”
Which move?
Use this for “Is it a flip, a slide or a turn?”
Congruent, similar or neither?
Use this for “Which figures are congruent to the first? Which are only similar?”