Teacher Page. 1. Reflect a figure with vertices across the x-axis. Find the coordinates of the new image.

Transcription

1 Teacher Page Geometr / Da # 10 oordinate Geometr (5 min.) 9-.G G G G.3. Use rigid motions (compositions of reflections, translations and rotations) to determine whether two geometric figures are congruent in a coordinate plane. Sketch a planar figure that is the result of given transformations (i.e. translation, reflection, rotation, and/or dilation) Identif similarit in terms of transformations Determine the effects of transformations on linear and area measurements of the original planar figure. 1. Reflect a figure with vertices across the -ais. Find the coordinates of the new image. a. b. c. d. 2. vertices (3, 1), (, 5), and (2, 3). Rotate 90 about the origin and then reflect it across the -ais. a. c. " ' ' " ' " " ' " " ' ' b. d. " ' " ' " " ' ' " " ' '

2 3. triangle is defined b the points (3, ), (10, -5), and (-9, -1). Sketch the triangle. Find the coordinates of the points after the triangle has been translated 7 units up In the answer bo provided, with words, graphs, tables or equations, show our solution to the problem. Onl work within the answer bo will be scored. 3.

3 . Graph the figure with coordinates at (,10), (6,-6), (-3,-), and D(-5,6).. Sketch its image under a dilation of 1 2 centered at the origin.. Find the coordinates In the answer bo provided, with words, graphs, tables or equations, show our solution to the problem. Onl work within the answer bo will be scored..

4 Ke Teacher Page Geometr / Da #10 oordinate Geometr (5 min.) 1. Reflect a figure with vertices across the -ais. Find the coordinates of the new image. a. b. (orrect nswer) c. d. Solution: The reflection of across the -ais is. D Feedback The reflection of (, ) on the -ais is (, ). orrect! The reflection of (, ) on the -ais is (, ). The reflection of (, ) on the -ais is (, ).

5 2. vertices (3, 1), (, 5), and (2, 3). Rotate 90 about the origin and then reflect it across the -ais. a. (orrect nswer) c. ' ' " " ' " " ' " " ' ' b. d. " ' " ' " " ' ' " " ' ' The rotation image of (, ) 90 counterclockwise is (, ), so (3, 1) ( 1, 3), (, 5) ( 5, ) and (2, 3) ( 3, 2). The reflection image of (, ) across the -ais is (, ), so ( 1, 3) ( 1, 3), ( 5, ) ( 5, ) and ( 3, 2) ( 3, 2). D Feedback orrect! This is a rotation of 90 clockwise about the origin and a reflection is across the -ais. This is a rotation of 10 about the origin, and then a reflection across the -ais. This is a reflection across the -ais, and then a rotation of 90 clockwise about the origin.

6 3. triangle is defined b the points (3, ), (10, -5), and (-9, -1). Sketch the triangle. Find the coordinates of the points after the triangle has been translated 7 units up. In the answer bo provided, with words, graphs, tables or equations, show our solution to the problem. Onl work within the answer bo will be scored (3, ) 10 ( 9, 1) (10, 5) 10 Solution: Original Triangle Sketched (1 Point) Translated triangle vertices (1 Point) (3, 11) (10, 2) (-9, 6)

7 . Graph the figure with coordinates at (,10), (6,-6), (-3,-), and D(-5,6). In the answer bo provided, with words, graphs, tables or equations, show our solution to the problem. Onl work within the answer bo will be scored.. Solution: Sketch Original Image (1 Point). Sketch its image under a dilation of 1 2 centered at the origin. (1 Point). Find the coordinates (2 Points) These points are obtained b multipling all original coordinates b ½.. (, 5) (3,-3) (-1.5,-2) D (-2.5, 3)

8 Name: Date: Per: Student Page: Geometr/ Da #10 oordinate Geometr 1. nn wants to create a design to decorate her Geometr binder. She reflects part of the design across line p and then reflects the image across line n. Describe a single transformation that moves the part of the design from its starting position to its final position. p Start n Finish a. rotation of 10 about the origin c. translation along the line b. rotation of 90 about the origin d. reflection across the line

9 2. Given the rectangle and the center of dilation P, which of the following is dilation with a scale factor of 2? P a. c. P P b. d. P P 3. In a dance performance, four dancers form a diamond with vertices. Then, the move along the dance floor following the translation vector,. There the pause, and then move again along the same vector. What are their coordinates after si such translations? a. b. c. d.

10 . Describe the dilation in the graph. ' ' ' In the answer bo provided, with words, graphs, tables or equations, show our solution to the problem. Onl work within the answer bo will be scored..

11 5. Find the coordinates of the image of the point (,6) when it is reflected across the line =11. a. (, -6) c. (, 16) b. (, -5) d. (, 17) 6. Find the translation of the triangle along. v a. c. b. d.

12 7. Rotate with vertices R(, 1), S(5, 3), and Q(3, 1) b 90 about the origin. a. c. S' R' S Q' S Q R' Q R Q' R S' b. d. S S' S Q Q' Q R R' R Q' R' S'

13 . State whether the transformation appears to be a translation. Provide specific reasons as to wh or wh not this transformation is a translation. If it does not appear to be a translation, state the correct transformation. In the answer bo provided, with words, graphs, tables or equations, show our solution to the problem. Onl work within the answer bo will be scored..

14 9. On a sketch of a mural, 3 inches represents one foot in the mural. door in the sketch is 2 inches wide b 5 inches high. What is the perimeter of the door in the mural epressed in inches? a. in. c. 20 in. b. in. d. 56 in. 10. triangle with vertices,, and is given. Which of the following is the image of the triangle under a dilation with a scale factor of centered at the origin? a. c. ' ' ' ' ' ' b. d. ' ' ' ' ' '

15 Ke Student Page Geometr / Da #10 oordinate Geometr 1. nn wants to create a design to decorate her Geometr binder. She reflects part of the design across line p and then reflects the image across line n. Describe a single transformation that moves the part of the design from its starting position to its final position. p Start n Finish a. rotation of 10 about the origin (orrect nswer) b. rotation of 90 about the origin c. translation along the line d. reflection across the line Solution: theorem, the composition of two reflections across intersecting lines is equivalent to a rotation about the point of intersection, and the angle of rotation is twice the measure of the angle between the lines. Since the lines are perpendicular, the form a 90 angle. The angle of rotation is. D Feedback orrect! Use the theorem about the compositions of two reflections across two intersecting lines to help ou. Use the theorem about the compositions of two reflections across two intersecting lines to help ou. Use the theorem about the compositions of two reflections across two intersecting lines to help ou.

16 2. Given the rectangle and the center of dilation P, which of the following is a dilation with a scale factor of 2? P a. (orrect nswer) c. P P b. d. P P Solution: Step 1 Draw a line through P and each verte. Step 2 On each line mark the point that is twice the distance from P to the verte. Step 3 onnect the vertices of the image. P ' D ' ' D' Feedback This rectangle is twice the width, but not twice the height. This rectangle is the right size, but the dilation is not centered at P. orrect! D This is a dilation with a scale factor of one half.

17 3. In a dance performance, four dancers form a diamond with vertices. Then, the move along the dance floor following the translation vector,. There the pause, and then move again along the same vector. What are their coordinates after si such translations? a. (orrect nswer) b. c. d. Solution: The complete translation is. D Feedback orrect! dd 2 to each -coordinate. dd 2 to each -coordinate. dd 2 to each -coordinate.. Describe the dilation in the graph ' ' ' In the answer bo provided, with words, graphs, tables or equations, show our solution to the problem. Onl work within the answer bo will be scored... Solution: (1 Point) Noting the coordinates of either,, or and the coordinates of the representative,, or from the dilated triangle. Such as (2, 1) and (6, 3) OR (, 1) and (, 3) OR (, -3) and (, -9). (1 Point) It is a dilation of 3 centered at the origin.

18 5. Find the coordinates of the image of the point (,6) when it is reflected across the line =11. a. (, -6) c. (, 16) (orrect nswer) b. (, -5) d. (, 17) Solution: (, 16 16) (, 6) image preimage D Feedback This is the point reflected over the -ais. Find the point reflected over the given line. Graph the point and the line of smmetr to help ou visualize the reflection. orrect! The reflected image should have the same distance.

19 6. Find the translation of the triangle along. v (orrect nswer) a. c. b. d. Solution: Step 1 Draw a line parallel to the vector through each verte of the triangle. Step 2 Measure the length of the vector. Then, from each verte mark off this distance in the same direction as the vector, on each of the parallel lines. v v

20 Step 3 onnect the image of the vertices. v D Feedback orrect! The vector v translates each point to the left three units, then up three units. The vector v translates each point to the left three units, then up three units. The vector v translates each point to the left three units, then up three units.

21 7. Rotate with vertices R(, 1), S(5, 3), and Q(3, 1) b 90 about the origin. a. (orrect nswer) c. S' R' S Q' S Q R' Q R Q' R S' b. d. S S' S Q Q' Q R R' R Q' R' S' Solution: The image of (, ) is (, ). R(, 1) (1, ) S(5, 3) ( 3, 5) Q(3, 1) ( 1, 3) Graph the preimage and the image. D Feedback orrect! The rotation is 90 counterclockwise, not clockwise. This is a rotation b 10 about the origin. This is a reflection across the -ais.

22 . State whether the transformation appears to be a translation. Provide specific reasons as to wh or wh not this transformation appears to be a translation. If it does not appear to be a translation, state the correct transformation and provide specific reasons that support the correct transformation. In the answer bo provided, with words, graphs, tables or equations, show our solution to the problem. Onl work within the answer bo will be scored.. Solution: This transformation does not appear to be a transformation. translation requires each point from the original figure to move the same distance and the same direction to the transformed figure. Each point has not moved the same distance and the same direction between the original figure and the transformed figure. (2 points) This transformation appears to be a reflection. reflection of the original image appears to be flipped across a line. (2 points) 9. On a sketch of a mural, 3 inches represents one foot in the mural. door in the sketch is 2 inches wide b 5 inches high. What is the perimeter of the door in the mural epressed in inches? a. in. c. 20 in. b. in. d. 56 in. (orrect nswer) Solution: ecause 3 inches on the sketch represents inches in the mural, the mural is a dilation of the sketch b a factor of. Find the dimensions of the door in the mural. Multipl each dimension b. in. in. Find the perimeter of the door. in. D Feedback This is the scale factor for the dilation. Now find the dimensions and the perimeter. This is the width of the door, now find the height and the perimeter. This is the height of the door, now find the width and the perimeter. orrect!

23 10. triangle with vertices,, and is given. Which of the following is the image of the triangle under a dilation with a scale factor of centered at the origin? a. (orrect nswer) c. ' ' ' ' ' ' b. d. ' ' ' ' ' '

24 Solution: The dilation of is Feedback orrect! Multipl the coordinates of each of the vertices b 3. Multipl the coordinates of each of the vertices b 3. D Multipl the coordinates of each of the vertices b 3.