Description

Pre-Algebra. Enlargements. 7.5. Multiply.1. 4 ?2. 12 ?3. 24 ? 4.

Transcripts

8 21 4 15 4. 3. 48 42 16 14 ? = n 12 45 18 = Quiz Tell whether this combine of proportions is relative. 1. Tackle the extent. 2. Discover two proportions that are comparable to each given ratio. Simplify to tell whether the proportions frame an extent. 16 10 32 20 5. also,

Dilations 7.5 Pre-Algebra

3 4 3 4 3 4 3 4 Warm Up Multiply. 1. 4 2. 12 3. 24 4. –36 9 3 18 –27 10 30 5. 4 2.5 6. 12 2.5

Learn to distinguish and make enlargements of plane figures.

Vocabulary widening scale consider focal point of enlargement

Your students are the dark territories in the focal point of your eyes. When you go to the eye specialist, the specialist may enlarge your students, which makes them bigger.

Translations, reflections, and turns are changes that don\'t change the size or state of a figure. An enlargement is a change that progressions the size, however not the shape, of a figure. A widening can broaden or decrease a figure.

A scale consider depicts how much a figure is developed or lessened. A scale variable can be communicated as a decimal, part, or percent. A 10% expansion is a scale element of 1.1, and a 10% decline is a scale element of 0.9.

Helpful Hint A scale calculate in the vicinity of 0 and 1 decreases a figure. A scale calculate more prominent than 1 extends it.

Example: Identifying Dilations Tell whether every change is an expansion. A. B. The change is not an enlargement. The figure is misshaped. The change is an expansion.

Example: Identifying Dilations Tell whether every change is a widening. C. D. The change is not an enlargement. The figure is contorted. The change is a widening.

A " An A " B " B " C " C " A B C Try This Tell whether every change is a widening. A. B. The change is not a widening. The figure is mutilated. The change is an enlargement.

An A " A " B C " B " B C " B " Try This Tell whether every change is a widening. D. C. The change is not a widening. The figure is contorted. The change is an expansion.

Every enlargement has a settled point that is the focal point of expansion . To locate the focal point of enlargement, draw a line that associates each match of relating vertices. The lines meet at a certain point. This point is the focal point of widening .

Example: Dilating a Figure Dilate the figure by a scale variable of 1.5 with P as the focal point of widening. Duplicate each side by 1.5.

G 1 cm 1 cm 2 cm 2 cm F\' H\' 1 cm F H 2 cm Try This Dilate the figure by a scale variable of 0.5 with G as the focal point of widening. G 2 cm 2 cm F H 2 cm Multiply each side by 0.5.

A\'B\'C\' A (4, 8) A \'(4 2 , 8 2 ) A \'(8, 16) B (3, 2) B \'(3 2 , 2 2 ) B \'(6, 4) C (5, 2) C \'(5 2 , 2 2 ) C \'(10, 4) ABC Example: Using the Origin as the Center of Dilation Dilate the figure in Example 3A on page 363 by a scale variable of 2. What are the vertices of the picture? Increase the directions by 2 to discover the vertices of the picture. The vertices of the picture are A \'(8, 16), B \'(6, 4), and C \'(10, 4).

Dilate the figure in Example 3B by a scale variable of . What are the vertices of the picture? 1 3 Multiply the directions by to discover the vertices of the picture. A\'B\'C\' C (6, 3) C \'(6 , 3 ) C \'(2, 1) B (9, 6) B \'(9 , 6 ) B \'(3, 2) A (3, 9) A \'(3 , 9 ) A \'(1, 3) ABC 1 3 1 3 1 3 1 3 1 3 1 3 1 3 Example: Using the Origin as the Center of Dilation The vertices of the picture are A \'(1, 3), B \'(3, 2), and C \'(2, 1).

Try This Dilate the figure by a scale element of 2. What are the vertices of the picture? 10 8 6 C 4 2 A B 10 8 4 6 2 0

A\'B\'C\' A (2, 2) A \'(2 2 , 2 2 ) A \'(4, 4) B (4, 2) B \'(4 2 , 2 2 ) B \'(8, 4) C (2, 4) C \'(2 2 , 4 2 ) C \'(4, 8) ABC Try This The vertices of the picture are A\'(4, 4), B\'(8, 4), and C\'(4, 8).

C\' B\' A\' Try This 10 8 6 C 4 2 B A 10 8 4 6 2 0

Try This Dilate the figure by a scale component of 0.5. What are the vertices of the picture? 10 C 8 6 B A 4 2 10 8 4 6 2 0

A (4, 5) A \'(4 0.5 , 5 0.5 ) A \'(2, 2.5) B (8, 5) B \'(8 0.5 , 5 0.5 ) B \'(4, 2.5) A\'B\'C\' ABC C (4, 9) C \'(4 0.5 , 9 0.5 ) C \'(2, 4.5) Try This The vertices of the picture are A\'(2, 2.5), B\'(4, 2.5), and C\'(2, 4.5).

C\' B\' A\' Try This 10 C 8 6 B A 4 2 10 8 4 6 2 0

1. Tell whether the change is an enlargement. A(0, 4) B(5,5) C(3,3) A\'(0, 8) B\'(10, 10) C\'(6, 6) P C " C A B " A " Lesson Quiz yes 2 4 6 2. Expand the figure by a scale variable of 1.5 with P as the focal point of widening. - 2 3. Widen the figure by a scale variable of 2 with the birthplace as the focal point of expansion. What are the directions of the picture? A (2,4) B (5,6) C (6,1) - 4 - 6 A \'(4,8) B \'(10,12) C \'(12,2)