Practice Dilation in Math

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

A transformation that enlarges or shrinks a figure by a scale factor from a center point.

Like zooming in or out on a photo—everything gets bigger or smaller proportionally.

Showing a random 20 of 50 problems.

Example 1

easy
A dilation has scale factor 3. By what factor does area change?

Example 2

hard
Two similar triangles have side ratio 2:52:5. What is the ratio of their areas?

Example 3

easy
What stays fixed during a dilation?

Example 4

hard
Why is the center of dilation the only fixed point (assuming k≠1k \ne 1)?

Example 5

medium
A rectangle has perimeter 3030. After a dilation by factor 23\tfrac{2}{3}, what is the new perimeter?

Example 6

medium
Does a dilation preserve orientation (for a positive scale factor)?

Example 7

medium
Point P(8,12)P(8, 12) is dilated from the origin with scale factor k=14k = \dfrac{1}{4}. Find the image P′P' and compare the distance from the origin to P′P' vs. to PP.

Example 8

challenge
Explain why a dilation (factor not 1) produces a similar but never congruent figure, and what single property makes it 'not rigid'.

Example 9

challenge
Does a dilation centered at a non-origin point preserve the origin?

Example 10

medium
A dilation maps (2,4)(2, 4) to (6,12)(6, 12) from the origin. Find the scale factor.

Example 11

hard
After dilation from the origin, segment AB‾\overline{AB} with A(2,1)A(2,1) and B(6,4)B(6,4) has image of length 2525. Find the scale factor.

Example 12

easy
Dilate (4,6)(4, 6) by scale factor 12\tfrac{1}{2} from the origin.

Example 13

challenge
A photograph 10 cm×15 cm10\text{ cm} \times 15\text{ cm} is enlarged so its area becomes 600 cm2600\,\text{cm}^2. Find the scale factor.

Example 14

easy
Dilate the point (10,−6)(10, -6) by scale factor 12\tfrac{1}{2} from the origin.

Example 15

medium
Dilate (3,4)(3, 4) by factor 22 from center (1,1)(1, 1).

Example 16

easy
What is the image of the origin under any dilation centered at the origin?

Example 17

easy
Dilate the point (3,2)(3, 2) by scale factor 2 from the origin.

Example 18

medium
Dilate (5,3)(5, 3) by factor 2 from the center (1,1)(1, 1).

Example 19

easy
Dilate the point (2,7)(2, 7) by scale factor 33 from the origin.

Example 20

hard
A scale model of a building uses scale factor 1100\tfrac{1}{100}. If the building has volume VV, what is the model's volume?
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