+ All Categories
Home > Documents > Lesson 4 Contents Example 1Translate a Figure Example 2Find a Translation Matrix Example 3Dilation...

Lesson 4 Contents Example 1Translate a Figure Example 2Find a Translation Matrix Example 3Dilation...

Date post: 27-Mar-2015
Category:

Documents
Upload: thomas-palmer
View: 263 times
Download: 4 times
Download Report this document
Share this document with a friend
Popular Tags:
coordinates of d
coordinates of f
translation matrix example
figure example
reflection example
coordinates of g
dilation example
contents example
22
Example 1 Translate a Figure Example 2 Find a Translation Matrix Example 3 Dilation Example 4 Reflection Example 5 Rotation
Transcript
Page 1: Lesson 4 Contents Example 1Translate a Figure Example 2Find a Translation Matrix Example 3Dilation Example 4Reflection Example 5Rotation.

Example 1 Translate a Figure

Example 2 Find a Translation Matrix

Example 3 Dilation

Example 4 Reflection

Example 5 Rotation

Page 2: Lesson 4 Contents Example 1Translate a Figure Example 2Find a Translation Matrix Example 3Dilation Example 4Reflection Example 5Rotation.

Find the coordinates of the vertices of the image of quadrilateral ABCD with A(–5, –1), B(–2, –1), C(–1, –4), and D(–3, –5) if it is moved 3 units to the right and 4 units up. Then graph ABCD and its image ABCD.

Write the vertex matrix for quadrilateral ABCD.

Page 3: Lesson 4 Contents Example 1Translate a Figure Example 2Find a Translation Matrix Example 3Dilation Example 4Reflection Example 5Rotation.

To translate the quadrilateral 3 units to the right, add 3 to each x-coordinate.

To translate the figure 4 units up, add 4 to each y-coordinate.

This can be done by adding the translation matrix

to the vertex matrix of ABCD.

Page 4: Lesson 4 Contents Example 1Translate a Figure Example 2Find a Translation Matrix Example 3Dilation Example 4Reflection Example 5Rotation.

Vertex Matrix Translation Vertex Matrix of ABCD Matrix of A'B'C'D'

The coordinates of ABCD are A(–2, 3), B(1, 3), C(2, 0), D(0, –1).

Graph the preimage and the image. The two graphs have the same size and shape.

Page 5: Lesson 4 Contents Example 1Translate a Figure Example 2Find a Translation Matrix Example 3Dilation Example 4Reflection Example 5Rotation.

Answer: A(–2, 3), B(1, 3), C(2, 0), D(0, –1)

Page 6: Lesson 4 Contents Example 1Translate a Figure Example 2Find a Translation Matrix Example 3Dilation Example 4Reflection Example 5Rotation.

Find the coordinates of the vertices of the image ofquadrilateral HIJK with H(2, 3), I(3, –1), J(–1, –3), and K(–2, 5) if it is moved 2 units to the left and 2 units up. Then graph HIJK and its image HIJK.Answer: H(0, 5), I(1, 1),

J(–3, –1), K(–4, 7)

Page 7: Lesson 4 Contents Example 1Translate a Figure Example 2Find a Translation Matrix Example 3Dilation Example 4Reflection Example 5Rotation.

Short-Response Test Item Rectangle EFGH is the result of a translation of the rectangle EFGH. A table of the vertices of each rectangle is shown. Find the coordinates of F and G.

Rectangle EFGH Rectangle EFGHE(–2, 2) E(–5, 0)

F F(1, 0)

G(4, –2) GH(–2, –2) H(–5, –4)

Page 8: Lesson 4 Contents Example 1Translate a Figure Example 2Find a Translation Matrix Example 3Dilation Example 4Reflection Example 5Rotation.

Read the Test Item

You are given the coordinates of the preimage and image of points E and H. Use this information to find the translation matrix. Then you can use the translation matrix to find the coordinates of F and G.

Page 9: Lesson 4 Contents Example 1Translate a Figure Example 2Find a Translation Matrix Example 3Dilation Example 4Reflection Example 5Rotation.

Solve the Test Item

Write a matrix equation. Let (a, b) represent the coordinates of F and let (c, d) represent the coordinates of G.

Page 10: Lesson 4 Contents Example 1Translate a Figure Example 2Find a Translation Matrix Example 3Dilation Example 4Reflection Example 5Rotation.

Since these two matrices are equal, corresponding elements are equal.

Solve an equation for x. Solve an equation for y.

Page 11: Lesson 4 Contents Example 1Translate a Figure Example 2Find a Translation Matrix Example 3Dilation Example 4Reflection Example 5Rotation.

Use the values for x and y to find the variables forF(a, b) and G(c, d).

Answer: So, the coordinates of F are (4, 2) and the coordinates of G are (1, –4).

Page 12: Lesson 4 Contents Example 1Translate a Figure Example 2Find a Translation Matrix Example 3Dilation Example 4Reflection Example 5Rotation.

Short-Response Test Item Rectangle ABCD is the result of a translation of the rectangle ABCD. A table of the vertices of each rectangle is shown. Find the coordinates of D and A.

Rectangle ABCD Rectangle ABCDA(–4, 5) AB(–1, 5) B(8, 0)

C(–1, 0) C(8, –5)

D D(5, –5)

Answer: The coordinates of D are (–4, 0) and the coordinates of A are (5, 0).

Page 13: Lesson 4 Contents Example 1Translate a Figure Example 2Find a Translation Matrix Example 3Dilation Example 4Reflection Example 5Rotation.

XYZ has vertices X(1, 2), Y(3, –1), and Z(–1, –2). Dilate XYZ so that its perimeter is twice the original perimeter. What are the coordinates of the vertices of XYZ?

If the perimeter of a figure is twice the original figure, then the lengths of the sides of the figure will be twice the measure of the original lengths. Multiply the vertex matrix by the scale factor of 2.

Page 14: Lesson 4 Contents Example 1Translate a Figure Example 2Find a Translation Matrix Example 3Dilation Example 4Reflection Example 5Rotation.

The coordinates of the vertices of XYZ are X(2, 4), Y(6, –2), and Z(–2, –4).

Graph XYZ and XYZ. The triangles are not congruent. The image has sides that are half the length of those of the original figure.

Answer: X(2, 4), Y(6, –2), Z(–2, –4)

Page 15: Lesson 4 Contents Example 1Translate a Figure Example 2Find a Translation Matrix Example 3Dilation Example 4Reflection Example 5Rotation.

ABC has vertices A(2, 1), B(–3, –2), and C(1, 4). Dilate ABC so that its perimeter is four times the original perimeter. What are the coordinates of the vertices of ABC?

Answer: A(8, 4), B(–12, –8), C(4, 16)

Page 16: Lesson 4 Contents Example 1Translate a Figure Example 2Find a Translation Matrix Example 3Dilation Example 4Reflection Example 5Rotation.

Find the coordinates of the vertices of the image of pentagon PENTA with P(–3, 1), E(0, –1), N(–1, –3), T(–3, –4), and A(–4, –1) after a reflection across the x-axis.

Write the ordered pairs as a vertex matrix. Then multiply the vertex matrix by the reflection matrix for the x-axis.

Page 17: Lesson 4 Contents Example 1Translate a Figure Example 2Find a Translation Matrix Example 3Dilation Example 4Reflection Example 5Rotation.

Answer: The coordinates of the vertices of PENTA areP(–3, –1), E(0, 1), N(–1, 3),T(–3, 4), and A(–4, 1). Noticethat the preimage and image arecongruent. Both figures have thesame size and shape.

Page 18: Lesson 4 Contents Example 1Translate a Figure Example 2Find a Translation Matrix Example 3Dilation Example 4Reflection Example 5Rotation.

Find the coordinates of the vertices of the image of pentagon PENTA with P(–5, 0), E(–3, 3), N(1, 2), T(1, –1), and A(–4, –2) after a reflection across the line y = x.

Answer: P(0, –5), E(3, –3), N(2, 1), T(–1, 1), A(–2, –4)

Page 19: Lesson 4 Contents Example 1Translate a Figure Example 2Find a Translation Matrix Example 3Dilation Example 4Reflection Example 5Rotation.

Find the coordinates of the vertices of the image of DEF with D(4, 3), E(1, 1), and F(2, 5) after it is rotated 90 counterclockwise about the origin.

Write the ordered pairs in a vertex matrix. Then multiply the vertex matrix by the rotation matrix.

Page 20: Lesson 4 Contents Example 1Translate a Figure Example 2Find a Translation Matrix Example 3Dilation Example 4Reflection Example 5Rotation.

Answer: The coordinates of the vertices of triangle DEF are D(–3, 4), E(–1, 1), and F (–5, 2). The image is congruent to the preimage.

Page 21: Lesson 4 Contents Example 1Translate a Figure Example 2Find a Translation Matrix Example 3Dilation Example 4Reflection Example 5Rotation.

Find the coordinates of the vertices of the image of TRI with T(–1, 2), R(–3, 0), and I(–2, –2) after it is rotated 180 counterclockwise about the origin.

Answer: T (1, –2), R(3, 0), I(2, 2)

Page 22: Lesson 4 Contents Example 1Translate a Figure Example 2Find a Translation Matrix Example 3Dilation Example 4Reflection Example 5Rotation.

Recommended
Pass - Jazz...Joe Pass JAZZ LINES REH VIDEO Example 1 Cmaj7 Example 2 Example 3 Example 4 Cmaj7 Example 5 H.O. P.o. Examplc 6 H.O. Example 7 H.O. H.O. H.O. Example 8 Crnaj7 Example

Pass - Jazz...Joe Pass JAZZ LINES REH VIDEO Example 1 Cmaj7 Example 2 Example 3 Example 4 Cmaj7 Example 5 H.O. P.o. Examplc 6 H.O. Example 7 H.O. H.O. H.O. Example 8 Crnaj7 Example

Documents

OFFICIAL BIKING GUIDE - Wisconsin Department of Tourism€¦ ·  · 2014-06-03OFFICIAL BIKING GUIDE EIGHTH EDITION. ... 2Find more fun at travelwisconsin.com or call 1-800/432-8747.

OFFICIAL BIKING GUIDE - Wisconsin Department of Tourism€¦ ·  · 2014-06-03OFFICIAL BIKING GUIDE EIGHTH EDITION. ... 2Find more fun at travelwisconsin.com or call 1-800/432-8747.

Documents

Lesson 6 Contents Example 1Multiply Powers Example 2Multiply Monomials Example 3Divide Powers Example 4Divide Powers Example 5Divide Powers to Solve a.

Lesson 6 Contents Example 1Multiply Powers Example 2Multiply Monomials Example 3Divide Powers Example 4Divide Powers Example 5Divide Powers to Solve a.

Documents

Example text 1 This is an example text. Example text. Example text 2 This is an example text. Example text. Example text 3 This is an example text. Example.

Example text 1 This is an example text. Example text. Example text 2 This is an example text. Example text. Example text 3 This is an example text. Example.

Documents

Lesson 3 Contents Example 1Translate Sentences into Equations Example 2Translate Sentences into Equations Example 3Translate Sentences into Equations Example.

Lesson 3 Contents Example 1Translate Sentences into Equations Example 2Translate Sentences into Equations Example 3Translate Sentences into Equations Example.

Documents

Fractions - Center For Teaching & Learningcontent.njctl.org/courses/math/7th-grade/review-of-6th-grade/... · 1Find the GCF of 18 and 44. l Slide 8 / 306 2Find the GCF of 72 and 75.

Fractions - Center For Teaching & Learningcontent.njctl.org/courses/math/7th-grade/review-of-6th-grade/... · 1Find the GCF of 18 and 44. l Slide 8 / 306 2Find the GCF of 72 and 75.

Documents

GENERAL HALLOWEEN · 2019-08-16 · cat 8 a cat Bean example cat 15 cat cute example cat 17 example cat 18 example Cat 31 example cat Dirty Duo example HappyYoureHom e example cat

GENERAL HALLOWEEN · 2019-08-16 · cat 8 a cat Bean example cat 15 cat cute example cat 17 example cat 18 example Cat 31 example cat Dirty Duo example HappyYoureHom e example cat

Documents

Unit 6: Polynomialsrotomath.weebly.com/uploads/1/2/1/6/121624811/unit_6_notes.pdfExercise 6: 2 a) Find the sum of 5x – 3x + 2 and 3x2 – 4x – 1. b) 2Find the sum of 7x 32– 3x

Unit 6: Polynomialsrotomath.weebly.com/uploads/1/2/1/6/121624811/unit_6_notes.pdfExercise 6: 2 a) Find the sum of 5x – 3x + 2 and 3x2 – 4x – 1. b) 2Find the sum of 7x 32– 3x

Documents

Splash Screen. Lesson Menu Objectives Vocabulary Example 1 Example 2 Example 3 Example 4 Quick Quiz.

Splash Screen. Lesson Menu Objectives Vocabulary Example 1 Example 2 Example 3 Example 4 Quick Quiz.

Documents

2Find Me Arabic

2Find Me Arabic

Documents

Trial Example Example Publication

Trial Example Example Publication

Documents

Splash Screen Lesson 9 Contents Obj. #1: Find the probability of simple events Example 1Find Probability Example 2Find Probability Example 3Find Experimental.

Splash Screen Lesson 9 Contents Obj. #1: Find the probability of simple events Example 1Find Probability Example 2Find Probability Example 3Find Experimental.

Documents

Math Pacing Guide 6 Unit 1 - Lorain City School District / …€¦ ·  · 2016-03-30more!detailed! “Learning!Targets ... 6.#G.A.2Find"thevolumeof"aright"rectangular"prism"with"fractional"edge"lengths"by"packing"it"with"unit"cubes"of"the"

Math Pacing Guide 6 Unit 1 - Lorain City School District / …€¦ ·  · 2016-03-30more!detailed! “Learning!Targets ... 6.#G.A.2Find"thevolumeof"aright"rectangular"prism"with"fractional"edge"lengths"by"packing"it"with"unit"cubes"of"the"

Documents

ERC Advanced Grant - FSI | CDDRL ·  · 2014-04-05ERC Advanced Grant 2013 Research proposal ... 2find only weak , or no, or sometimes even negative, correlations between these standard

ERC Advanced Grant - FSI | CDDRL ·  · 2014-04-05ERC Advanced Grant 2013 Research proposal ... 2find only weak , or no, or sometimes even negative, correlations between these standard

Documents

Practice Test 1 · 2019-04-03 · 25. Write the equation of a line given by 6x – 3y + 9 = 0 in slope-intercept form (i.e., in the form y = mx + b). 26. 2Find the volume of a triangular

Practice Test 1 · 2019-04-03 · 25. Write the equation of a line given by 6x – 3y + 9 = 0 in slope-intercept form (i.e., in the form y = mx + b). 26. 2Find the volume of a triangular

Documents

Propositional Logic Example Example Example · Propositional Logic Example Example Example Consider the following sentences: 1 If it rains, the aquaphobes won’t vote 2 John will

Propositional Logic Example Example Example · Propositional Logic Example Example Example Consider the following sentences: 1 If it rains, the aquaphobes won’t vote 2 John will

Documents

St Andrew’s Academy ·  · 2017-12-133. 2Find the roots of : x x + −=4 1 0 . We cannot factorise : x x: 2 +−41 , but we can use the quadratic formula: 2 ( ) 4: ... there are

St Andrew’s Academy ·  · 2017-12-133. 2Find the roots of : x x + −=4 1 0 . We cannot factorise : x x: 2 +−41 , but we can use the quadratic formula: 2 ( ) 4: ... there are

Documents

TRO Example - TRO Example

TRO Example - TRO Example

Documents