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3. Tell whether the transformation is a dilation. A(0, 4) B(5,5) C(3,3) A’(0, 8) B’(10, 10) C’(6, 6). Quiz. Use the properties of similar figures to answer 1 and 2:.

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3. Tell whether the transformation is a dilation.

A(0, 4) B(5,5) C(3,3) A’(0, 8) B’(10, 10) C’(6, 6)

QuizUse the properties of similar figures to answer 1 and 2:

1. A rectangular house is 32 ft wide and 68 ft long. On a blueprint, the width is 8 in. Find the length on the blueprint.

2. Karen enlarged a 3 in. wide by 5 in. tall photo into a poster. If the poster is 2.25 ft wide, how tall is it?

4. Dilate the figure by a scale factor of 2 with the origin as the center of dilation. What are the coordinates of the image? A(2,4) B(5,6) C(6,1)

4

1

10

2

1

5

4

Warm UpEvaluate the following for x = 16.

1.3x2.x

Evaluate the following for x = .

3. 10x4.x

48

12

4

Learn to make comparisons between and find dimensions of scale drawings and actual objects.

Scale and Scale Drawings

A scale drawing is a two-dimensional drawing that accurately represents an object. The scale drawing is mathematically similar to the object.

A scale gives the ratio of the dimensions in the drawing to the dimensions of the object. All dimensions are reduced or enlarged using the same scale. Scales can use the same units or different units.

The scale a:b is read “a to b.” For example, the scale 1 cm:3 ft is read “one centimeter to three feet.”

1 4

1 4

Scale - InterpretationSet up proportion using

8 m

1 cm

x m

scale length .

actual length

Example: Using Proportions to Find Unknown Scales or LengthsA. The length of an object on a scale drawing is 2 cm, and its actual length is 8 m. The scale is 1 cm: __ m. What is the scale?

=

1 8 = x 2

Find the cross products.

8 = 2x

4 = x

Solve the proportion.

The scale is 1 cm:4 m.

Set up proportion using

x ft

1 in.

6 ft

scale length .

actual length

Example: Using Proportions to Find Unknown Scales or LengthsB. The length of an object on a scale drawing is 1.5 inches. The scale is 1 in:6 ft. What is the actual length of the object?

=

1 x = 6 1.5

Find the cross products.

x = 9

Solve the proportion.

The actual length is 9 ft.

Set up proportion using

12 m

1 cm

x m

scale length .

actual length

Try ThisA. The length of an object on a scale drawing is 4 cm, and its actual length is 12 m. The scale is 1 cm: __ m. What is the scale?

=

1 12 = x 4

Find the cross products.

12 = 4x

3 = x

Solve the proportion.

The scale is 1 cm:3 m.

Set up proportion using

x ft

1 in.

4 ft

scale length .

actual length

Try ThisB. The length of an object on a scale drawing is 2 inches. The scale is 1 in:4 ft. What is the actual length of the object?

=

1 x = 4 2

Find the cross products.

x = 8

Solve the proportion.

The actual length is 8 ft.

Reductions and Enlargements

A scale drawing that is smaller than the actual object is called a reduction. A scale drawing can also be larger than the object. In this case, the drawing is referred to as an enlargement.

=

x mm

1000

1

scale length

actual length

Example: Life Sciences ApplicationUnder a 1000:1 microscope view, an amoeba appears to have a length of 8 mm. What is its actual length?

1000 x = 1 8

Find the cross products.

x = 0.008

Solve the proportion.

The actual length of the amoeba is 0.008 mm.

=

x mm

10,000

1

scale length

actual length

Try ThisUnder a 10,000:1 microscope view, a fiber appears to have length of 1mm. What is its actual length?

10,000 x = 1 1

Find the cross products.

x = 0.0001

Solve the proportion.

The actual length of the fiber is 0.0001 mm.

A drawing that uses the scale in. = 1 ft is said to be in in. scale. Similarly, a drawing that uses the scale in. = 1 ft is in in. scale.

1 4

1 4

1 2

1 2

What does it Mean?A. If a wall in a in. scale drawing is 4 in. tall, how tall is the actual wall?

1

=

4

4 in.

x ft.

0.25 in.

1 ft

scale length

actual length

Example: Using Scales and Scale Drawings to Find HeightsLength ratios are equal.

Find the cross products.

0.25 x = 1 4

Solve the proportion.

x = 16

The wall is 16 ft tall.

1 tall is the actual wall?

=

2

4 in.

x ft.

0.5 in.

1 ft

scale length

actual length

Example: Using Scales and Scale Drawings to Find HeightsB. How tall is the wall if a in. scale is used?

Length ratios are equal.

Find the cross products.

0.5 x = 1 4

Solve the proportion.

x = 8

The wall is 8 ft tall.

A. If a wall in a in. scale drawing is 0.5 in. thick, how thick is the actual wall?

1

=

4

0.5 in.

x ft.

0.25 in.

1 ft

scale length

actual length

Try ThisLength ratios are equal.

Find the cross products.

0.25 x = 1 0.5

Solve the proportion.

x = 2

The wall is 2 ft thick.

1 thick is the actual wall?

=

2

0.5 in.

x ft.

0.5 in.

1 ft

scale length

actual length

Try This ContinuedB. How thick is the wall if a in. scale is used?

Length ratios are equal.

Find the cross products.

0.5 x = 1 0.5

Solve the proportion.

x = 1

The wall is 1 ft thick.

1 thick is the actual wall?

4

Lesson Quiz1. What is the scale of a drawing in which a 9 ft wall is 6 cm long?

2. Using a in. = 1 ft scale, how long would a drawing of a 22 ft car be?

3. The height of a person on a scale drawing is 4.5 in. The scale is 1:16. What is the actual height of the person?

The scale of a map is 1 in. = 21 mi. Find each length on the map.

4. 147 mi 5. 5.25 mi

1 cm = 1.5 ft.

5.5 in.

72 in.

7 in.

0.25 in.

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