Transformation Packet

Transcription

1 Name Transformation Packet UE: TEST: 1

2 . Transformation Vocabular Transformation Related Terms Sketch Reflection (flip across a line) Line of reflection Pre-image and image Rigid Rotation (turn about a point in a specific direction) Translation (shifted cop) Point of rotation egrees lockwise or counterclockwise Rigid Vertical and horizontal shift Rigid ilation (reduction or enlargement) Scale factor Not rigid 2

3 oordinate Transformation Rules raw the image of rectangle under each transformation. escribe the transformation in words! List the points of the image of rectangle (the image is called rectangle ). 1. (, ) (, ) 2. (, ) (, ) 3. (, ) ( 3, ) 4. (, ) (, + 4) 5. (, ) ( 2, 1) 6. (, ) (, ) 3

4 7. (, ) (, ) 8. (, ) (, ) 9. (, ) (0.5, 0.5) 10. (, ) ( 0.5, 0.5) oes the order in which a point is transformed matter?? Let s see (, ) ( 2, + 3) (, ) 12. (, ) (, ) ( 2, + 3) What can ou infer from eamples 11 and 12? 4

5 Summar of oordinate Transformations Eample: escribe the transformation using coordinate notation. Eample: Find the coordinates of the vertices of triangle after the transformation (,) (,-). ( 3,4) (, ) (2, 1) (, ) ( 1, 5) (, ) Eample: raw with vertices (4, 0), (0, 4), and (0, 0). Then find the coordinates of the vertices of the image after the translation (, ) ( 4, 3), and draw the image. Eample: Find the coordinates of line segment after the transformation (,) (2,2). (5,2) (, ) ( 8, 4) (, ) 5

6 Rectangle has coordinates (1,6), ( 5, 2), ( 1, 5), and (5,3). Graph rectangle. Rectangle is the result of transforming rectangle based on the rule (,) (2,2). What is the name of this transformation? etermine the coordinates for (use the rule above): = = = = Graph on the coordinate plane at right. ompare the graphs of and. Find the length of the four sides of rectangle (use the distance formula). = = = = Find the area of rectangle. Find the length of the four sides of rectangle (use the distance formula). = = = = Find the area of rectangle. ompare the side lengths and areas of and. e specific. What do ou notice about the location of as compared to? Hopefull this eample will help eplain wh the LOTION of a figure changes under a dilation. 6

7 In the eample on the previous page, ou determined the coordinates of after the transformation (,) (2,2). This transformation is called a. Recop the coordinates of below. etermine the distance of each point above from the origin O(0,0). O O O O onsider the original coordinates of rectangle given below. (1,6) ( 5, 2) ( 1, 5) (5,3) etermine the distance of each point above from the origin O(0,0). O O O O ompare O and O O and O O and O. nd O and O. So a dilation not onl changes the length of sides of a figure, but changes the location of each point making up the figure b. 7

8 Practice 1. Find the coordinates of the vertices of the image after the specified transformation, and draw the image. (, ) ( 4, +2) (, ) (, ) (, ) (0.5, 0.5) 2. Transformations can be used to show motion. Use coordinate notation to describe the transformation of the drummer from one picture to the net picture. 3. raw one triangle with vertices (2, 1), (3, 4), and (4, 1) and a second triangle with vertices (4, 1), (3, 4), and (2, 1).escribe two different transformations that could move the first triangle onto the second. 8

9 4. The vertices of quadrilateral are (3, 4), (2, 4), (3, 2), and (4, 1). fter a translation, the coordinates of are (5, 1). escribe the translation using coordinate notation. Then find the coordinates of,, and. 5. etermine whether or not the following statements are TRUE or FLSE. a. The transformation (,) (+2, +2) applied to the ordered pairs that form a square will result in a square that covers twice the area of the original square. b. The transformation (,) (,-2) will translate a figure left 2 units. c. When reflected over the -ais, the point (3, 5) becomes (3,5). d. When reflected over the -ais, the point (3, 5) becomes (3,5). e. If square has ( 4,1) and is rotated 90 clockwise about the origin, then the new coordinates of must be (1,4). f. Translating a figure results in a figure similar, but not congruent to the original figure. g. Rotating a figure results in a figure congruent to the original figure. h. The onl transformation that results in a figure similar, but not congruent to the original figure is a dilation. 6. MULTIPLE HOIE Rectangle is the image of rectangle after which of the following rotations?. 90 clockwise rotation about the origin. 90 counterclockwise rotation about the origin. 180 rotation about the origin. reflection over the -ais. 9

10 7. The vertices of triangle are ( 3, 1), ( 4,3), and (1,2). Reflect the triangle over the line =. Graph the triangle and its image. 8. The vertices of quadrilateral are (5, 2), (7, 4), (4, 7), and (2, 5). Rotate the figure 90 counterclockwise. Graph the figure and its image. 8. In the diagram, the quadrilateral is rotated about P. What is the value of? 9. Graph EF with vertices (0,3), E(4,3), and F(0,6). Then graph its image after translating according to the rule (,) (, +2), then rotating

11 1. Which rotation will carr a square onto itself? a. 30 clockwise rotation b. 45 counterclockwise rotation c. 60 clockwise rotation d. 90 counterclockwise rotation 2. Which rotation will carr a regular heagon onto itself? a. 30 clockwise rotation b. 90 counterclockwise rotation c. 120 clockwise rotation d. 330 counterclockwise rotation 3. Which rotation will carr a regular octagon onto itself? a. 30 counterclockwise rotation b. 120 counterclockwise rotation c. 135 clockwise rotation d. 300 clockwise rotation N FINL Practice 4. Which rotation will carr a regular decagon onto itself? a. 45 clockwise rotation b. 72 counterclockwise rotation c. 90 clockwise rotation d. 148 counterclockwise rotation 5. If triangle is translated 5 units down and 3 units left, which transformation would move it back to its original location? a. (, ) ( + 3, + 5) b. (, ) ( 3, 5) c. (, ) ( + 5, + 3) d. (, ) ( 5, 3) 6. If triangle is rotate 90 clockwise, which transformation would move it back to its original location? a. (, ) (, ) b. (, ) (, ) c. (, ) (, ) d. (, ) (, ) 7. MN has M(1,9) and N(5,12). If MN is dilated with respect to the origin b a scale factor of k to produce M N, which statement must be true? a. M N has a length of 5. b. The midpoint of M N is (3,10.5). c. The line that passes through M and N has a slope of ( 3 4 ) k. d. The line that passes through M and N intersects the -ais at (0,8.25k). 8. Triangle EGF is graphed below. Triangle EGF will be rotated 90 clockwise around the origin and will then be reflected across the -ais, producing an image triangle. Which additional transformation will map the image triangle back onto the original triangle? rotation 270 counterclockwise around the origin rotation 180 counterclockwise around the origin reflection across the line = reflection across the line = 11

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