Dilations And Similarity Basics

1) Which of these dilations is a reduction?

Scale factor 2

Scale factor 1

Scale factor 5

Scale factor 0.75

Reductions have 0 < k < 1.

Explanation

Reductions have 0 < k < 1.

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

7

12

4

3

New length = 3 × 4 = 12.

Explanation

New length = 3 × 4 = 12.

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

(2, 3)

(8, 12)

(6, 9)

(1, 2)

(4,6) scaled by 1/2 → (2,3).

Explanation

(4,6) scaled by 1/2 → (2,3).

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

Rigid motion

Enlargement or reduction that preserves shape

Translation

Reflection

Dilations change size while keeping angles and proportions.

Explanation

Dilations change size while keeping angles and proportions.

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

(6, 10)

(1.5, 2.5)

(5, 3)

(0, 2)

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

Explanation

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

6) 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:

(1, 2), (2, 3), (3, 1)

(4, 8), (8, 12), (12, 4)

(0.5, 1), (1, 1.5), (1.5, 0.5)

(2, 2), (4, 3), (3, 1)

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

Explanation

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

7) A dilation with a scale factor greater than 1 will:

Shrink the figure

Enlarge the figure

Keep the figure the same size

Flip the figure

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

Explanation

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

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

1.5 by 2

2 by 4

3 by 2

6 by 8

6×0.25 = 1.5 and 8×0.25 = 2.

Explanation

6×0.25 = 1.5 and 8×0.25 = 2.

9) A dilation with a scale factor less than 1 but greater than 0 will:

Enlarge the figure

Shrink the figure

Reflect the figure

Rotate the figure

If 0 < k < 1, all lengths are multiplied by k, so they get smaller.

Explanation

If 0 < k < 1, all lengths are multiplied by k, so they get smaller.

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

(x/k, y/k)

(x, ky)

(k + x, k + y)

(kx, ky)

About the origin, multiply each coordinate by k.

Explanation

About the origin, multiply each coordinate by k.

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

Side lengths

Angles

Perimeter

Area

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

Explanation

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

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

Angles change but sides remain equal

Angles are preserved and sides are proportional

Angles and side lengths remain identical

The figure rotates 90°

That’s the definition of similarity under dilation.

Explanation

That’s the definition of similarity under dilation.

13) Which statement is true about dilations?

They always move figures to a different location.

They always preserve angle measures.

They always preserve lengths.

They always rotate figures.

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

Explanation

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

14) A dilation always creates figures that are:

Congruent

Not related

Similar

Rotated

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

Explanation

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

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

Produce a smaller figure

Produce a larger figure

Produce a congruent figure

Eliminate the figure

k = 1 leaves size and shape unchanged.

Explanation

k = 1 leaves size and shape unchanged.

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

2

0.5

1

25

New length = 0.2 × 5 = 1.

Explanation

New length = 0.2 × 5 = 1.

17) The scale factor is the ratio of:

New area to original area

New perimeter to original perimeter

New side length to original side length

New angle to original angle

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

Explanation

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

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

DE ÷ D′E′

D′E′ ÷ DE

Area of DEF ÷ Area of D′E′F′

Perimeter of DEF ÷ Perimeter of D′E′F′

Scale factor = image side / preimage side.

Explanation

Scale factor = image side / preimage side.

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

48

144

36

9

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

Explanation

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

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

5/2

8/20

2/5

15/8

k = 20 ÷ 8 = 5/2 = 2.5.

Explanation

k = 20 ÷ 8 = 5/2 = 2.5.

Dilations and Similarity Basics

1) Which of these dilations is a reduction?

2)

What first name or nickname would you like us to use?

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

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

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

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

6) 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:

7) A dilation with a scale factor greater than 1 will:

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

9) A dilation with a scale factor less than 1 but greater than 0 will:

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

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

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

13) Which statement is true about dilations?

14) A dilation always creates figures that are:

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

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

17) The scale factor is the ratio of:

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

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

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