Geometry. Transformations. Slide 1 / 154 Slide 2 / 154. Slide 4 / 154. Slide 3 / 154. Slide 6 / 154. Slide 5 / 154. Transformations.

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1 Slide 1 / 154 Slide 2 / 154 Geometry Transformations Slide 3 / 154 Slide 4 / 154 Table of ontents click on the topic to go to that section Transformations Translations Reflections Rotations omposition of Transformations ongruence Transformations ilations Similarity Transformations Transformations Return to Table of ontents Slide 5 / 154 Transformations transformation of a geometric figure is a mapping that results in a change in the position, shape, or size of the figure. In the game of dominoes, you often move the dominoes by sliding them, turning them or flipping them. Each of these moves is a type of transformation. Slide 6 / 154 Transformations In a transformation, the original figure is the preimage, and the resulting figure is the image. In the examples below, the preimage is green and the image is pink. translation - slide rotation - turn reflection - flip

2 Slide 7 / 154 Transformations Some transformations (like the dominoes) preserve distance and angle measures. These transformations are called rigid motions. To preserve distance means that the distance between any two points of the image is the same as the distance between the corresponding points of the preimage. Slide 8 / 154 Transformations Which of these is a rigid motion? Translation- slide Rotation-turn To preserve angles means that the angles of the image have the same measures as the corresponding angles in the preimage. Reflection- Flip ilation - Size change Slide 9 / 154 Slide 10 / 154 transformation maps every point of a figure onto its image and may be described using arrow notation ( ). Prime notation (' ) is sometimes used to identify image points. Transformations In the diagram below, ' is the image of. ' 1 oes the transformation appear to be a rigid motion? Explain. Yes, it preserves the distance between consecutive points. No, it does not preserve the distance between consecutive points. ' # # ''' # maps onto # ''' Note: You list the corresponding points of the preimage and image in the same order, just as you would for corresponding points in congruent figures or similar figures. ' Preimage Image Slide 11 / oes the transformation appear to be a rigid motion? Explain. Yes, distances are preserved. Yes, angle measures are preserved. oth and. No, distance are not preserved. Slide 12 / Which transformation is not a rigid motion? Reflection Translation Rotation Preimage Image ilation

3 Slide 13 / Which transformation is demonstrated? Reflection Translation Rotation ilation Slide 14 / Which translation is demonstrated? Reflection Translation Rotation ilation Slide 15 / 154 Slide 16 / Which transformation is demonstrated? Reflection Translation Rotation Translations ilation Return to Table of ontents Slide 17 / 154 Translations translation is a transformation that maps all points of a figure the same distance in the same direction. Slide 18 / 154 Translations Write the translation that maps onto ''' as T( ) = ''' translation is a rigid motion with the following properties: ' ' = ' = ' = '', = '', = '' m< = m<', m< = m<', m< = m<' ' '

4 Slide 19 / 154 Translations in the oordinate Plane Each (x, y) pair in is mapped to (x + 9, y - 4). You can use the function notation T <9,-4>() = '''' to describe the translation. is translated 9 units right and 4 units down. ' ' ' ' Slide 20 / 154 Finding the Image of a Translation What are the vertices of T <-2, 5> ( Graph the image of EF. ' ( ) E' ( ) F' ( ) raw ', EE' and FF'. What relationships exist among these three segments? EF)? E F How do you know? Slide 21 / 154 Writing a Translation Rule Write a translation rule that maps PQRS P'Q'R'S'. Slide 22 / In the diagram, Δ''' is an image of Δ. Which rule describes the translation? P T <-5,-3>( ) T <5,3>( ) P' S Q T <-3,-5>( ) S' Q' R T <3,5>( ) R' Slide 23 / If T <4,-6>(JKLM) = J'K'L'M', what translation maps J'K'L'M' onto JKLM? T <4,-6>(J'K'L'M') T <6,-4>(J'K'L'M') T <6,4>(J'K'L'M') T <-4,6>(J'K'L'M') Slide 24 / RSV has coordinates R(2,1), S(3,2), and V(2,6). translation maps point R to R' at (-4,8). What are the coordinates of S' for this translation? (-6,-4) (-3,2) (-3,9) (-4,13) E none of the above

5 Slide 25 / 154 Slide 26 / 154 Reflection reflection is a transformation of points over a line. This line is called the line of reflection. The result looks like the preimage was flipped over the line. The preimage and the image have opposite orientations. Reflections Reflections ctivity Lab (lick for link to lab) m ' ' ' If a point is on line m, then the image of is itself ( = '). If a point is not on line m, then m is the perpendicular bisector of ' Return to Table of ontents The reflection across m that maps Δ Δ''' can be written as R m( Δ ) = Δ'' Slide 27 / 154 When reflecting a figure, reflect the vertices and then draw the sides. Reflect over line r. Label the vertices of the image. Reflection r lick here to see a video Slide 28 / 154 Reflection Reflect WXYZ over line s. Label the vertices of the image. W Z X Y s Hint: Turn page so line of symmetry is vertical Slide 29 / 154 Reflection Slide 30 / Which point represents the reflection of X? Reflect MNP over line t. Label the vertices of the image. M Where is the image of N? Why? point point point point X t N P E None of the above

6 Slide 31 / Which point represents the reflection of X? Slide 32 / Which point represents the reflection of X? point point point point point E none of the above X point point point E none of the above X Slide 33 / Which point represents the reflection of? point Slide 34 / Is a reflection a rigid motion? Yes point point No point E none of these Slide 35 / 154 Reflections in the oordinate Plane Since reflections are perpendicular to and equidistant from the line of reflection, we can find the exact image of a point or a figure in the coordinate plane. Slide 36 / 154 Reflections in the oordinate Plane Reflect,, & over the y-axis. How do the coordinates of each point change when the point is reflected over the y-axis? Notation R y-axis() = ' R y-axis() = ' R y-axis() = '

7 Slide 37 / 154 Reflections in the oordinate Plane Slide 38 / 154 Reflections in the oordinate Plane Reflect figure JKLM over the x-axis. Notation R x-axis (JKLM) = J'K'L'M' M J K L Reflect,, & over the line y = x. Notation R y=x R y=x () = ' () = ' R y=x R y=x () = ' () = ' How do the coordinates of each point change when the point is reflected over the x-axis? How do the coordinates of each point change when the point is reflected over the y-axis? Slide 39 / 154 Reflections in the oordinate Plane Slide 40 / 154 Reflections in the oordinate Plane Reflect Δ over x = 2. Reflect quadrilateral MNPQ over y = -3 N Notation R x=2( Δ) = Δ''' Notation R Y=-3(MNPQ) = M'N'P'Q' M Q P *Hint: draw line of reflection first Slide 41 / 154 Find the oordinates of Each Image 1. R x-axis() Slide 42 / The point (4,2) reflected over the x-axis has an image of. (4,2) 2. R y-axis() 3. R y=1() F (-4,-2) (-4,2) 4. R x=-1() 5. R y=x(e) E (4,-2) 6. R x=-2(f)

8 Slide 43 / The point (4,2) reflected over the y-axis has an image of. (4,2) (-4,-2) (-4,2) (4,-2) Slide 44 / has coordinates (-3,0). What would be the coordinates of ' if is reflected over the line x = 1? (-3,0) (4,0) (-3,2) (5,0) Slide 45 / The point (4,2) reflected over the line y=2 has an image of. (4,2) Slide 46 / 154 Line of Symmetry line of symmetry is a line of reflection that divides a figure into 2 congruent halves. These 2 halves reflect onto each other. (4,1) (2,2) (4,-2) Slide 47 / 154 raw Lines of Symmetry Where pplicable E F Slide 48 / 154 raw Lines of Symmetry Where pplicable M N O P Q R

9 Slide 49 / 154 raw Lines of Symmetry Where pplicable Slide 50 / How many lines of symmetry does the following have? one two three none Slide 51 / How many lines of symmetry does the following have? Slide 52 / How many lines of symmetry does the following have? infinitely many none one nine infinitely many Slide 53 / How many lines of symmetry does the following have? Slide 54 / How many lines of symmetry does the following have? none none one two J one two H infinitely many infinitely many

10 Slide 55 / 154 Slide 56 / How many lines of symmetry does the following have? none Rotations Rotations ctivity Lab (lick for link to lab) Return to Table of ontents Slide 57 / 154 Rotations rotation is a rigid motion that turns a figure about a point. The amount of turn is in degrees. The direction of turn is either clockwise or counterclockwise. H P Slide 58 / 154 rotation of x, about a point P is a transformation with the following properties: - The image of P is itself (P = P') - For any other point, P' = P -The m <P' = x Rotations -The preimage and its image ' are `equidistant from the center of rotation. P' P x ' ' ' The arrow was rotated counterclockwise about point P. The heart was rotated clockwise about H. r (x, P)( Δ) = Δ''' for a rotation clockwise x about P r (-x, P)( Δ ) = Δ ''' for a rotation counterclockwise x about P Slide 59 / 154 rawing Rotation Images What is the image of r (100, )( Step 1 raw O. Use a protractor to draw a 100 angle with side O and vertex. Step 2 Use a compass or a ruler to construct O # O' Step 3 Locate L' and ' following steps 1 and 2. Step 4 raw L'O'' O L LO)? lick here to see video Slide 60 / 154 rawing Rotation Images What is the image of r (80, )( LO)? (clockwise) O L

11 Slide 61 / 154 Rotations in the oordinate Plane When a figure is rotated 90, 180, or 270 clockwise about the origin O in the coordinate plane, you can use the following rules: r (90, O)(x, y) = (y, -x) Slide 62 / 154 Rotations in the oordinate Plane When a figure is rotated 90, 180, or 270 clockwise about the origin O in the coordinate plane, you can use the following rules: r (180, O)(x, y) = (-x, -y) r (-270, O)(x, y) = r (90, O)(x, y) (3, 4) (3, 4) ' (4, -3) ' (-3, -4) Slide 63 / 154 Rotations in the oordinate Plane When a figure is rotated 90, 180, or 270 clockwise about the origin O in the coordinate plane, you can use the following rules: Slide 64 / 154 Rotations in the oordinate Plane When a figure is rotated 90, 180, or 270 clockwise about the origin O in the coordinate plane, you can use the following rules: r (270, O)(x, y) = (-y, x) r (360, O)(x, y) = (x, y) r (-90, O)(x, y) = r (270, O)(x, y) ' (-4, 3) (3, 4) ' (3, 4) Slide 65 / 154 Graphing Rotation Images PQRS has vertices P(1, 1), Q(3, 3), R(4, 1) and S(3, 0). a) What is the graph of r (90,0)(PQRS) = P'Q'R'S'? Slide 66 / 154 Graphing Rotation Images PQRS has vertices P(1, 1), Q(3, 3), R(4, 1) and S(3, 0). b) What is the graph of r (90,0)(PQRS) = P''Q''R''S''?

12 Slide 67 / 154 Graphing Rotation Images PQRS has vertices P(1, 1), Q(3, 3), R(4, 1) and S(3, 0). c) What is the graph of r (270,0)(PQRS)= P'''Q'''R'''S'''? Slide 68 / Square has vertices (3,3), (-3,3), (-3, -3), and (3, -3). Which of the following images is? r (90,0)() r (180,0)() r (90,0)() r (270,0)() Slide 69 / PQRS has vertices P(1,5), Q(3, -2), R(-3, -2), and S(-5, 1). What are the coordinates of Q' after r (270,0)(Q)? (-2, -3) (2,3) (-3, 2) (-3, -2) Slide 70 / 154 Identifying a Rotation Image regular polygon has a center that is equidistant from its vertices. Segments that connect the center to the vertices divide the polygon into congruent triangles. You can use this fact to find rotation images of regular polygons. PENT is a regular pentagon with center O. a) Name the image of E for a 72 rotation counterclockwise about O. b) Name the image of P for a 216 rotation clockwise about O. O P E c) Name the image of P for a 144 rotation counterclockwise about O. T N Slide 71 / MTH is a regular quadrilateral with center R. Name the image of M for a 180º rotation counterclockwise about R. M T H R M Slide 72 / MTH is a regular quadrilateral with center R. Name the image of for a 270º rotation clockwise about R. H M R H M M

13 Slide 73 / HEXGO is a regular hexagon with center M. Name the image of G for a 300º rotation counterclockwise about M. H E Slide 74 / HEXGO is a regular hexagon with center M. Name the image of OH for a 240º rotation clockwise about M. HE H E X E O M X G EX O M X H E O G X E OG G Slide 75 / 154 Slide 76 / 154 Rotational Symmetry figure has rotational symmetry if there is at least one rotation less than or equal to 180º about a point so that the preimage is the image. For example, a 3-bladed fan has a rotational symmetry at 120º. circle has infinite rotational symmetry. Rotational Symmetry o the following have rotational symmetry? If yes, what is the degree of rotation? a. c. b. Slide 77 / 154 Rotational Symmetry o the following regular shapes have rotational symmetry? If yes, what is the degree of rotation? Slide 78 / oes the following figure have rotational symmetry? If yes, what degree? yes, 90º yes, 120º yes, 180º S no In general, what is the rule that can be used to find the degree of rotation for a regular polygon?

14 Slide 79 / oes the following figure have rotational symmetry? If yes, what degree? yes, 90º yes, 120º yes, 180º no Slide 80 / oes the following figure have rotational symmetry? If yes, what degree? yes, 90º yes, 120º yes, 180º no Slide 81 / 154 Slide 82 / oes the following figure have rotational symmetry? If yes, what degree? yes, 18º yes, 36º yes, 72º omposition of Transformations no Return to Table of ontents Slide 83 / 154 Isometry When an image is used as the preimage for a second transformation it is called a composition of transformations. The transformations below are isometries. n isometry is transformation that preserves distance or length. Slide 84 / 154 Isometry The transformations below are isometries. The composition of two or more isometries is an isometry. Reflection Glide Reflection Translation Rotation

15 Slide 85 / 154 Glide Reflections If two figures are congruent and have opposite orientations (but are not simply reflections of each other), then there is a translation and a reflection that will map one onto the other. glide reflection is the composition of a glide (translation) and a reflection across a line parallel to the direction of translation. Slide 86 / 154 Glide Reflections Graph the glide reflection image of Δ. 1.) R x- axis o T <-2, 0> ( Δ) Notation for a omposition R y = -2 o T <1, 0> ( Δ) Note: Transformations are performed right to left. ' ' ' Slide 87 / 154 Glide Reflections Graph the glide reflection image of Δ. 2.) R y- axis o T <0, -3> ( Δ) Slide 88 / 154 Glide Reflections Graph the glide reflection image of Δ. 3.) R y = -1 o T <1, -1> ( Δ) X Y Z Slide 89 / 154 omposition of Reflections Translate ΔXYZ by using a composition of reflections. Reflect over x = -3 then over x = 4. Label the first image ΔX'Y'Z' and the second ΔX"Y"Z". 1.) What direction did ΔXYZ slide? How is this related to the lines of reflection? Slide 90 / FGHJ is translated using a composition of reflections. FGHJ is first reflected over line r then line s. How far does FGHJ slide? r 5" 10" 15" F G H J s Make a conjecture. 2.)How far did ΔXYZ slide? How is this related to the lines of reflection? 20" 10"

16 Slide 91 / FGHJ is translated using a composition of reflections. FGHJ is first reflected over line r then line s. Which arrow shows the direction of the slide? r F G H J 10" s Slide 92 / FGHJ is translated using a composition of reflections. FGHJ is first reflected over line s then line r. How far does FGHJ slide? r 5" 10" 20" 30" F G H J 10" s Slide 93 / 154 Rotations as omposition of Reflection Where the lines of reflection intersect, P, is center of rotation. P 80 o m ' ' 160 o " ' " n " The amount of rotation is twice the acute,or right, angle formed by the lines of reflection. Slide 94 / 154 Rotations as omposition of Reflection If E is reflected over r then s: What is the angle of rotation? What is the direction of the rotation? E 20º r s The direction of rotation is clockwise because rotating from m to n across the acute angle is clockwise. Had the triangle reflected over n then m, the rotation would have been counterclockwise. Slide 95 / 154 Rotations as omposition of Reflection If E is reflected over s then r: What is the angle of rotation? What is the direction of the rotation? E 20º r s Slide 96 / 154 Rotations as omposition of Reflection If E is reflected over s then r: What is the angle of rotation? What is the direction of the rotation? 90º E r s

17 Slide 97 / 154 Rotations as omposition of Reflection If E is reflected over s then r: What is the angle of rotation? What is the direction of the rotation? s 110º E r Slide 98 / If the image of Δ is the composite of reflections over e then f, what is the angle of rotation? 40º 80º 160º 280º 40º e f Slide 99 / What is the direction of the rotation if the image of Δ is the composite of reflections first over e then f? Slide 100 / If the image of Δ is the composite of reflections over f then e, what is the angle of rotation? lockwise ounterclockwise 40º e f 90º 180º 270º e 360º f Slide 101 / What is the direction of rotation if the image of Δ is the composite of reflections first over f then e? lockwise ounterclockwise e Slide 102 / If the image of Δ is the composite of reflections over e then f, what is the angle of rotation? 40º 80º 140º 160º 140º e f f

18 Slide 103 / 154 Slide 104 / What is the direction of the rotation if the image of Δ is the composite of reflections first over e then f? lockwise ounterclockwise e ongruence Transformations 140º Return to Table of ontents Slide 105 / 154 ongruent Figures Two figures are congruent if and only if there is a sequence of one or more rigid motions that maps one figure onto another. The composition R m o T <2, 3> Since compositions of rigid motions preserve angle measures and distances the corresponding sides and angles have equal measures. Fill in the blanks below: = ' = = m# = m# m# = m# m# = m# (# ) = (# EF) ' ' E m F Slide 106 / 154 Identifying ongruence Transformations ecause compositions of rigid motions take figures to congruent figures, they are also called congruence transformations. What is the congruence transformation that maps ΔXYZ to Δ? Z X Y s Slide 107 / 154 Using ongruence Transformations Use congruence transformations to verify that Δ # ΔEF Slide 108 / 154 Using ongruence Transformations To show that Δ is an equilateral triangle, what congruence transformation can you use that maps the triangle onto itself? Explain. n P p m

19 Slide 109 / Which congruent transformation maps Δ to ΔEF? T <-5,5> Slide 110 / Which congruence transformation does not map Δ to ΔEF? Slide 111 / Which of the following best describe a congruence transformation that maps Δ to ΔEF? a reflection only a translation only a translation followed by a reflection a translation followed by a rotation F Slide 112 / Quadrilateral is shown below. Which of the following transformations of ΔE could be used to show that ΔE is congruent to ΔE? a reflection over a reflection over line m a reflection over a reflection over line n m E n E Slide 113 / 154 Slide 114 / 154 ilation dilation is a transformation whose pre image and image are similar. Thus, a dilation is a similarity transformation. It is not, in general, a rigid motion. ilations Return to Table of ontents Pupil ilated Pupil Every dilation has a center and a scale factor n, n > 0. The scale factor describes the size change from the original figure to the image.

20 Slide 115 / 154 ilation dilation with center R and scale factor n, n > 0, is a transformation with the following properties: ' ' dilation is an enlargement if the scale factor is greater than 1. Slide 116 / Types of ilations dilation is a reduction if the scale factor is less than one, but greater than 0. R'=R - The image of R is itself (R' = R) - For any other point, ' is on R - R' = n R or n = R' R - Δ ~ Δ''' ' scale factor of 2 scale factor of 1.5 scale factor of 3 scale factor of 3/4 scale factor of 1/2 scale factor of 1/4 Slide 117 / 154 Slide 118 / 154 ilations Finding the Scale Factor The symbol for scale factor is n. 6 ' 18 ' dilation is an enlargement if n > 1. dilation is a reduction if 0< n < ' ' What happens to a figure if n = 1? The ratio of corresponding sides is image = preimage which is the scale factor (n) of the dilation. orresponding angles are congruent. Slide 119 / 154 ilations The dashed line figure is a dilation image of the solid-line figure. is the center of dilation. Tell whether the dilation is an enlargement or a reduction. Then find the scale factor of the dilation. Slide 120 / 154 ilations The dashed line figure is a dilation image of the solid-line figure. is the center of dilation. Tell whether the dilation is an enlargement or a reduction. Then find the scale factor of the dilation. 1 2 Reduction; NSWER1/2 NSWER Reduction; 3/2 6 Enlargement; NSWER Enlargement; NSWER 2 Enlargement; 2 NSWER

21 48 Is a dilation a rigid motion? Yes No Slide 121 / 154 Slide 122 / Is the dilation an enlargement or a reduction? What is the scale factor of the dilation? enlargement, n = 3 enlargement, n = 1/3 reduction, n = 3 8 F reduction, n = 1/3 24 F' Slide 123 / Is the dilation an enlargement or reduction? What is the scale factor of the dilation? Slide 124 / Is the dilation an enlargement or reduction? What is the scale factor of the dilation? enlargement, n=3 enlargement, n = 2 H 2 enlargement, n = 1/3 reduction, n = 3 F' 8 enlargement, n = 1/2 reduction, n = 2 H' 4 reduction, n = 1/3 F 24 reduction, n = 1/2 Slide 125 / Is the dilation an enlargement or reduction? What is the scale factor of the dilation? enlargement, n = 2 enlargement, n = 3 enlargement, n = 6 not a dilation 5 R' R Slide 126 / The solid-line figure is a dilation of the dashed-line figure. The labeled point is the center of dilation. Find the scale factor of dilation /2 1/3 X 3 6

22 Slide 127 / dilation maps triangle LMN to triangle L'M'N'. MN = 14 in. and M'N' = 9.8 in. If LN = 13 in., what is L'N'? 13 in. 14 in. 9.1 in. 9.8 in. Steps Slide 128 / 154 rawing ilation Images raw the dilation image Δ (2, 1. Use a straightedge to construct ray X. 2. Use a compass to measure X. 1 in 3.onstruct X' by constructing a congruent segment on ray X so that X' is twice the distance of X. 4.Repeat steps 1-3 with points and. 0.5 in X 2.5 in X )(Δ) 5 in ' ' lick here to watch a video ' Slide 129 / 154 Slide 130 / 154 raw Each ilation Image a. ) (0.5, )() b. ) (2, )(ΔEF) ilations in the oordinate Plane Suppose a dilation is centered at the origin. You can find the dilation image of a point by multiplying its coordinates by the scale factor. Scale factor 2, (x, y) (2x, 2y) Notation 2 () = ' ' (4, 6) (2, 3) NSWER NSWER Slide 131 / 154 Graphing ilation Images To dilate a figure from the origin, find the dilation images of its vertices. ΔHJK has vertices H(2, 0), J(-1, 0.5), and K(1, -2). What are the coordinates of the vertices of the image of ΔHJK for a dilation with center (0, 0) and a scale factor 3? Graph the image and the preimage. Slide 132 / 154 ilations NOT entered at the Origin ' ' ' ' In this example, the center of dilation is NOT the origin. The center of dilation (-2, -2) is a vertex of the original figure. This is a reduction with scale factor 1/2. Point and its image are the same. It is important to look at the distance from the center of dilation, to the other points of the figure. If = 6, then '' = 6/2 = 3. lso notice = 4 and '' = 2, etc.

23 F Slide 133 / 154 ilations E raw the dilation image of ΔEF with the center of dilation at point with a scale factor 3/4. Slide 134 / What is the y-coordinate of the image (8, -6) under a dilation centered at the origin and having a scale factor of 1.5? Slide 135 / 154 Slide 136 / What is the x-coordinate of the image (8, -6) under a dilation centered at the origin and having a scale factor of 1/2? 57 What is the y-coordinate of the image (8, -6) under a dilation centered at the origin and having a scale factor of 1/2? Slide 137 / What is the x-coordinate of the image of (8, -6) under a dilation centered at the origin and having a scale factor of 3? Slide 138 / What is the x-coordinate of the image of (8, -6) under a dilation centered at the origin and having a scale factor of 1.5?

24 Slide 139 / What is the y-coordinate of the image of (8, -6) under a dilation centered at the origin and having a scale factor of 3? Slide 140 / What is the x-coordinate of (4, -2) under a dilation centered at (1, 3) with a scale factor of 2? Slide 141 / 154 Slide 142 / What is the y-coordinate of (4, -2) under a dilation centered at (1, 3) with a scale factor of 2? Similarity Transformations 8 Return to Table of ontents Slide 143 / 154 Warm Up 1. hoose the correct choice to complete the sentence. Rigid motions and dilations both preserve angle measure / distance. 2. omplete the sentence by filling in the blanks. rigid motions dilations preserve distance; do not preserve distance. 3. efine similar polygons on the lines below. Slide 144 / 154 Triangle GHI has vertices G(-4, 2), H(-3, -3) and N(-1, 1). Suppose the triangle is translated 4 units right and 2 units up and then dilated by a scale factor of 2 with the center of dilation at the origin. Sketch the resulting image of the composition of transformations. Step 1 raw the original figure. Step 2 T <4, 2> G' (, ) H' (, ) I' (, ) Step 3 2 (ΔG'H'I') G" (, ) H"(, ) I" (, ) (ΔGHI) rawing Transformations

25 Slide 145 / 154 rawing Transformations Δ LMN has vertices L(0, 2), M(2, 2), and N(0, 1). For each similarity transformation, draw the image o R x -axis ( ΔLMN ) Slide 146 / 154 rawing Transformations ΔLMN has vertices L(0, 2), M(2, 2), and N(0, 1). For each similarity transformation, draw the image o r (270, O) ( ΔLMN ) Slide 147 / 154 escribing Transformations What is a composition of transformations that maps trapezoid onto trapezoid MNHP? Slide 148 / 154 escribing Transformations For each graph, describe the composition of transformations that maps Δ onto ΔFGH 1. G F H Slide 149 / 154 escribing Transformations For each graph, describe the composition of transformations that maps Δ onto ΔFGH G Slide 150 / 154 Similar Figures Two figures are similar if and only if there is a similarity transformation that maps one figure onto the other. Identify the similarity transformation that maps one figure onto the other and then write a similarity statement. 9 N 4 P in. in. 6 in. 6 in. M Q N M L J K F H Rotate quadrilateral 90 counterclockwise ilate it by nswer a scale factor of 2/3 Translate it so that vertices and M coincide. ~ MNPQ Rotate # LMN 180 so that the vertical angles coincide. ilate it by nswer some scale factor x so that MN and JK coincide. # LMN ~ # LJK

26 Slide 151 / Which similarity transformation maps Δ to ΔEF? Slide 152 / Which similarity transformation does not map ΔPQR to ΔSTU? Slide 153 / 154 Slide 154 / Which of the following best describes a similarity transformation that maps ΔJKP to ΔLMP? M J a dilation only L a rotation followed by a dilation a reflection followed by a dilation a translation followed by a dilation P K