Dilations and Similarity Basics

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Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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| Attempts: 17 | Questions: 20 | Updated: Jan 19, 2026
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1) A dilation with a scale factor greater than 1 will:

Explanation

Scale factor k > 1 makes every length k times larger.

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About This Quiz
Dilations and Similarity Basics - Quiz

Are you ready to see how shapes can grow or shrink but keep the same look? In this quiz, you’ll learn what a dilation does, how a scale factor changes size, and why angles stay the same while sides stay in proportion. You’ll practice resizing shapes by multiplying their coordinates... see moreby a scale factor, figure out if the dilation makes them bigger or smaller, and see how this creates similar figures.
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2) A dilation with a scale factor less than 1 but greater than 0 will:

Explanation

If 0

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3) A dilation with a scale factor of 1 will:

Explanation

k = 1 leaves size and shape unchanged.

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4) Which of the following remains unchanged during a dilation?

Explanation

Dilations preserve angle measures. Side lengths, perimeter, and area scale (by k, k, and k²).

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5) Triangle ABC is dilated by a factor of 3. If side AB was 4 units, what is the new length of AB′?

Explanation

New length = 3 × 4 = 12.

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6) A dilation centered at the origin with scale factor 2 transforms point (3, 5). The new point is:

Explanation

Multiply coordinates by k = 2: (2×3, 2×5) = (6, 10).

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7) A triangle with vertices (2, 4), (4, 6), (6, 2) is dilated by a factor of 0.5 about the origin. The new coordinates are:

Explanation

Multiply by 0.5: (2,4)→(1,2), (4,6)→(2,3), (6,2)→(3,1).

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8) Which statement is true about dilations?

Explanation

Lengths change unless k = 1; angles stay the same.

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9) Which of these dilations is a reduction?

Explanation

Reductions have 0

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10) Which of the following best describes a dilation of a polygon?

Explanation

Dilations change size while keeping angles and proportions.

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11) A line segment of length 5 is dilated by a factor of 0.2. The new length is:

Explanation

New length = 0.2 × 5 = 1.

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12) The scale factor is the ratio of:

Explanation

Scale factor k = (image length)/(preimage length).

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13) A rectangle with dimensions 6 by 8 is dilated with a scale factor of 0.25. The new dimensions are:

Explanation

6×0.25 = 1.5 and 8×0.25 = 2.

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14) The image of a square under dilation is similar to the original square because:

Explanation

That’s the definition of similarity under dilation.

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15) A point (x, y) dilated by a factor of k becomes:

Explanation

About the origin, multiply each coordinate by k.

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16) A dilation always creates figures that are:

Explanation

Dilations produce similar figures (congruent only when k = 1).

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17) If point A (4, 6) is dilated by a factor of 1/2 about the origin, what is A′?

Explanation

(4,6) scaled by 1/2 → (2,3).

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18) If the preimage is triangle DEF and the image is triangle D′E′F′, then the scale factor is:

Explanation

Scale factor = image side / preimage side.

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19) A figure has an area of 16 square units. After a dilation with scale factor 3, what is the new area?

Explanation

Area scales by k²: 16 × 3² = 16 × 9 = 144.

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20) The scale factor of a dilation that maps a triangle with side length 8 to a triangle with side length 20 is:

Explanation

k = 20 ÷ 8 = 5/2 = 2.5.

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Cierra Henderson |MBA |
K-12 Expert
Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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A dilation with a scale factor greater than 1 will:
A dilation with a scale factor less than 1 but greater than 0 will:
A dilation with a scale factor of 1 will:
Which of the following remains unchanged during a dilation?
Triangle ABC is dilated by a factor of 3. If side AB was 4 units, what...
A dilation centered at the origin with scale factor 2 transforms point...
A triangle with vertices (2, 4), (4, 6), (6, 2) is dilated by a factor...
Which statement is true about dilations?
Which of these dilations is a reduction?
Which of the following best describes a dilation of a polygon?
A line segment of length 5 is dilated by a factor of 0.2. The new...
The scale factor is the ratio of:
A rectangle with dimensions 6 by 8 is dilated with a scale factor of...
The image of a square under dilation is similar to the original square...
A point (x, y) dilated by a factor of k becomes:
A dilation always creates figures that are:
If point A (4, 6) is dilated by a factor of 1/2 about the origin, what...
If the preimage is triangle DEF and the image is triangle...
A figure has an area of 16 square units. After a dilation with scale...
The scale factor of a dilation that maps a triangle with side length 8...
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