SME
Grade 10 Math · Problem type
Dilation from a center
Use this for “Dilate an 8 by 6 rectangle by a scale factor of 0.5 from the point O.”
Diagram
Dilation from O by scale factor 0.5: each image corner is 0.5 times as far from O, on the same ray
A factor under 1 shrinks the figure toward O
Width: 8 × 0.5 = 4
Height: 6 × 0.5 = 3
This is an example. Type your own values to start a new problem.
W
=
k
×
w
H
=
k
×
h
Formulas
W
=
k
×
w
4 = 0.5 × 8
H
=
k
×
h
3 = 0.5 × 6
Assumptions
•
The center O is 2 squares left of and 1 square below the figure’s bottom left corner.
•
Each image point is on the ray from O through the original point, k times as far from O.
•
A factor over 1 enlarges, under 1 shrinks; every length is multiplied by k.
Step-by-step
WE KNOW
k = 0.5, w = 8, h = 6
FIND
image width (W), image height (H)
Step 1 · Find image width (W)
Use W = k × w
Multiply the width by the scale factor.
W
=
0.5
×
8
W
=
4
Step 2 · Find image height (H)
Use H = k × h
Multiply the height by the scale factor.
H
=
0.5
×
6
H
=
3
Check
Put the numbers back in. Both sides should match.
4 = 0.5 × 8 ✓
3 = 0.5 × 6 ✓
Topic check
See what you know: 5 questions on this topic
New questions each time. Pass to mark it complete.
Refresh
Translations, rotations, reflections and dilations
Proportional relationships and the constant of proportionality
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Similarity: dilations and similar triangles
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