Chapter 9 Retake Test (GH)

Transcription

1 Name: Period: Date: Chapter 9 Retake Test (GH) 1 The hexagon GIKMPR and FJN are regular. The dashed line segments form 30 angles. Find the angle of rotation about O that maps L to J. 2 The vertices of a triangle are P(1, 2), Q( 7, 4), and R( 7, 2). Name the vertices of the image reflected across the x-axis. 3 The vertices of a triangle are P( 4, 3), Q( 2, 3), and R(7, 3). Name the vertices of the image reflected across the line y = x. 4 Find the translation that moves trapezoid 1 to trapezoid 2 and the translation that moves trapezoid 3 to trapezoid 4. 5 Find the coordinates of the image of ABC after the glide reflection described. Translation: Ê Áx, yˆ Ê Áx 4, yˆ ; Reflection: in y = 1 6 Quadrilateral WXYZ has vertices WÊ Á 5, 2 ˆ, X Ê Á 2, 1ˆ, Y Ê Á0, 3ˆ, and Z Ê Á 3, 4 ˆ. Reflect the quadrilateral in the line y= x. 7 What is the order of the symmetry of the pizza shown below? 1

2 8 Find the translation rule that describes the translation B D. 10 Reflect AB over the x-axis and rotate 90 about the origin. Find the endpoints of the image of AB. 9 The transformation Ê Áx, yˆ Ê Á x, yˆ is applied to the figure below. Graph the image of the figure under this transformation. 11 Find the image vertices for a dilation with center (0, 0) and a scale factor of The vertices of a triangle are P( 5, 2), Q(1, 1), and R(8, 8). Name the vertices of the image reflected across the y-axis. 13 A figure is translated using the vector 6, 1. What translation vector would move the image back to its original position? 14 Michael is about 6 feet tall, and the length of his shadow is about 3 feet. What is the scale factor of the shadow? 15 The blades of a propeller exhibit rotational symmetry. Identify the order and magnitude of the symmetry of the blades of the propeller in the figure. 2

3 16 Graph the figure and its image under the given translation. JK with endpoints J(2, 3), K(1, 5) under the translation (x, y) (x 4, y+ 1). 20 Find the image of ABC after the glide reflection described. Translation: Ê Áx, yˆ Ê Áx+ 1, yˆ ; Reflection: in y= 1 17 For the figure below, draw all the lines of symmetry. If there are none, write "none." 18 Find the scale factor of the dilation. Then tell whether the dilation is a reduction or an enlargement. 19 The pattern exhibits rotational symmetry. Identify the order and magnitude of the symmetry of the pattern. 21 P P (8, 6) for the glide reflection where the translation is (x,y) (x 1,y 5) and the line of reflection is y = x. Find the coordinates of P. 22 Richard brought a life-size cardboard cutout of a football player. If the original photograph used to make that cutout was 6 inches in height and the height of the cutout was 72 inches, then what was the scale factor of the cutout? 23 State whether the following figure has line symmetry, rotational symmetry, both kinds of symmetry, or neither kind of symmetry. 3

4 24 PQ below is rotated counterclockwise 90 about the origin. Find the coordinates of the endpoints of the image PQ. 30 The dashed-lined triangle is a dilation image of the solid-lined triangle. Is the dilation an enlargement or a reduction? What is the scale factor of the dilation? 25 Graph DEF with vertices DÊ Á 0, 3 ˆ, E Ê Á4, 3ˆ, and F Ê Á 0, 7 ˆ. Then graph its image after the given transformation. Rotate 180. Then translate using Ê Á x, y ˆ Ê Á x 1, y 1 ˆ. 31 The transformation Ê Áx, yˆ Ê Á y, xˆ is applied to the figure below. Graph the image of the figure under this transformation. 26 Draw the image of the given figure after a dilation with center O and the given scale factor. scale factor: Graph points A(1, 5), B(5, 2), and C(1, 2). Graph image of ABC reflected across the line x= A person in a car travels 7 miles south and then 12 miles west. The person realized she was lost and so she resumed traveling 12 miles north and 10 miles east. Give the component form for the vector that represents the overall path of the car. 33 The vertices of ABC are AÊ Á 3, 1 ˆ, B Ê Á 4, 3ˆ, and C Ê Á 1, 2 ˆ. Reflect the triangle in the line y= x. Graph the triangle and its image. 28 A photo originally measuring 11 inches by 9 inches needs to be enlarged to a size of 55 by 45 inches. Find the scale factor of the enlarged photo. 29 Which type of isometry is the equivalent of two reflections across intersecting lines? 4

5 34 Tell whether the three-dimensional object has rotational symmetry about a line and/or reflectional symmetry in a plane. 39 The translation vector is uç = 7, 4. If the image of A is A Ê Á6, 4ˆ, find the coordinates of point A. 40 What are the images of the vertices of ABC for a dilation with center (0, 0) and scale factor 1.5? 35 How many lines of symmetry does a rhombus that is not a square have? 36 Find the vertices of the image after the indicated composition of transformations. YZ: Y(3,6) and Z(1,1) Reflection: in y-axis Rotation: 180 about origin 41 Determine the scale factor for each dilation. Determine whether the dilation is an enlargement, reduction, or congruence transformation. 37 Find the coordinates of the image of a triangle with vertices A(0, 6), B( 3, 0), and C(4, 1) for a rotation of 270 counterclockwise about the origin. 38 Find the scale factor of the dilation. Then tell whether the dilation is a reduction or an enlargement. 42 How many lines of symmetry does a regular hexagon have? 43 The vertices of a rectangle are R( 5, 5), S( 1, 5), T( 1, 1), and U( 5, 1). After translation, R is the point ( 8, 10). Find the translation rule (coordinate form) and coordinates of U. 44 Reflect AB over the y-axis and rotate 180 about the origin. A(5, -1) B(1, -3) 5

6 45 Find the vector, vç, that will translate ABC onto A B C. 50 Find the image of ABC after the glide reflection described. Translation: Ê Á x, y ˆ Ê Á x, y+ 2 ˆ ; Reflection: in x= 2 46 How many lines of symmetry does the figure have? 51 Find the scale factor of the dilation. Then tell whether the dilation is a reduction or an enlargement. 47 Find the vertices of the image after the indicated glide reflection. Triangle DEF has vertices of D(2, 2), E(5, 3), and F(3, 4). Translate along 0, 3 and reflect in the y-axis. 48 A triangle has vertices P( 5, 4), Q( 5, 0), R(0, 0). PQR is rotated counterclockwise 270 about the origin. Find the coordinates of the vertices of the image PQR. 49 Describe in words the translation represented by the translation rule (x, y) (x+ 3, y+ 7). 52 Use a translation rule to describe the translation (coordinate form) that is 4 units to the left and 10 units down. 53 The dashed-lined figure is a dilation image of the solid-lined figure. Is the dilation an enlargement, or a reduction? What is the scale factor of the dilation? 6

7 54 The figure shows a kitchen exhaust fan. Find the order and magnitude of the symmetry of the logo. 55 Draw the image of the given figure after a dilation with center O and the given scale factor. scale factor: 2 56 Find the image of O( 2, 1) after two reflections, first across the line y = 3, and then across the line x= 1. 7

8 Chapter 9 Retake Test (GH) Answer Section P (1, 2), Q ( 7, 4), R ( 7, 2) 3 P ( 3, 4), Q (3, 2), R (3, 7) (x,y) Ê Áx 2, y+ 5ˆ, 3 4 (x,y) Ê Áx+ 5, y 6ˆ 5 6 W' Ê Á 2,5 ˆ, X' Ê Á 1,2ˆ, Y' Ê Á3,0ˆ, and Z' Ê Á 4,3 ˆ (x, y) (x+ 7, y+ 2) 9 10 A (5, 2), B (2, 4) 11 A ( 6, 2), B (8, 6), C (4, 6), D ( 2, 8) 12 P (5, 2), Q ( 1, 1), R ( 8, 8) 13 6,

9 15 Order 6 and magnitude 60 Order is the number of rotations a figure makes. Magnitude is 360 divided by the order. 16 J' ( 2,4), K' ( 3,6) ; enlargement 19 Order 5 and magnitude 72 Order is the number of rotations a figure makes. Magnitude is 360 divided by the order. 20 A' ( 1,4) A"( 1,0) B' (2,4) B"(2,0) C' (6,7) C"(6, 3) 21 ( 5, 3) rotational 24 P (0, 2); Q ( 1, 5) 25 D' (0, 3) D"( 1, 4) E' ( 4, 3) E"( 5, 4) F' (0, 7) F"( 1, 8) 26 Image coordinates: ( ), (-3, 0), (-2.5, -2.5), (0, , rotation 30 reduction; 1 2 2

10 31 32 A' ( 5, 1), B' ( 2, 5), C' ( 2, 1) 33 A' ( 1, 3), B' (3, 4), C' (2,1) 34 reflectional symmetry and rotational symmetry Y (3, 6), Z (1, 1) Y(3,6) Y ( 3,6) Z(1,1) Z ( 1,1) Y ( 3,6) Y (3, 6) Z ( 1,1) Z (1, 1) 37 A (6, 0), B (0, 3), C ( 1, 4) ; reduction 39 (13, 8) 40 A( 2,4) ((1.5) ( 2),(1.5) (4)), or A ( 3,6) B(4,2) ((1.5) (4),(1.5) (2)), or B (6,3) C( 4, 4) ((1.5) ( 4),(1.5) ( 4)), or C ( 6, 6) 41 2; enlargement (x, y) (x 3, y 5); ( 8, 4) 44 A (5, 1), B (1, 3) 45 vç = 6,

11 47 D ( 2, 1), E ( 5,0), F ( 3,1) D(2,2) D (2, 1) E(5,3) E (5,0) F(3,4) F (3,1) D (2, 1) D ( 2, 1) E (5,0) E ( 5,0) F (3,1) F ( 3,1) 48 P (-4, 5), Q (0, 5), R (0, 0) 49 3 units to the right and 7 units up 50 A' (4,5) A"(0,5) B' (8,6) B"( 4,6) C' (3,8) C"(1,8) 51 3; enlargement 52 (x,y) (x 4,y 10) 53 3; enlargement 54 order 3 and magnitude 120 Order is the number of rotations a figure makes. Magnitude is 360 divided by the order. 55 Image Coordinates; (2, 3), (3, -2), (-4, 0) 56 (0, 7) 4