Rotations: Lesson 4 Grid & Coordinates Name
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- Heather Fleming
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1 In this lesson, you will investigate the coordinates of vertices of rotated triangles and look for patterns. Open the document: Rotations.tns. It is important that the Rotations Tour be done before any Rotations lessons. PLAY INVESTIGATE EXPLORE DISCOVER Move to page 1.3. ( / two times) On the handheld, press / and / to navigate through the pages of the lesson. (On the ipad, select the page thumbnail in the page sorter panel.) 1. Press b to open the menu. (On the ipad, tap the wrench icon to open the menu.) Press 1 (1: Templates), 5 (5: Grid & Coordinates). 2. Rotate a triangle about the origin through angles of 90 o, 180 o, 270 o, and 360 o and look for patterns among the coordinates. Change the angle of rotation to 90 o. the space bar (_) to select 90 o and to close the menu. or press Q to rotate ABC 90 o about the origin. a. Record the Original coordinates (first coordinates displayed) in the first row of the table on the next page. Look for patterns. b. Investigate and mentally make note of the coordinates by grabbing and moving each of the Record a set of data observed in row Figure 1 in the following table. Repeat and move each of the three vertices and record a set of data in row Figure 2 in the following table. Suggestion: Move point A to Quadrant II and move point C to Quadrant IV. Look for patterns among the coordinates of corresponding vertices. Which coordinates remain the same? Which coordinates change? How? Discuss Texas Instruments Incorporated 1 education.ti.com
2 Rotate 90 o A B C A B C Original Figure 1 Figure 2 c. Using the pattern observed in the previous table, if a point on the pre-image triangle has coordinates (5, 8), what are the coordinates of the corresponding point on the image triangle? That is (5, 8) means maps to Similarly, the point ( 3, 7) would map to what point? That is ( 3, 7). d. In general, if a point on the pre-image triangle has coordinates (x, y), what are the coordinates of the corresponding point on the image triangle? That is (x, y) means maps to 3. Reset the page. Press (/. ). Change the angle of rotation to 180 o. the space bar (_) to select 180 o and to close the menu. or press Q to rotate ABC 180 o about the origin. a. Record the Original coordinates (first coordinates displayed) in the first row of the following table. Look for patterns. b. Investigate and mentally make note of the coordinates by grabbing and moving each of the Record a set of data observed in row Figure 1 in the following table. Repeat and move each of the three vertices and record a set of data in row Figure 2 below. Suggestion: Move point A to Quadrant IV and move point C to Quadrant II. Look for patterns among the coordinates of corresponding vertices. Which coordinates remain the same? Which coordinates change? How? Discuss. Rotate 180 o A B C A B C Original Figure 1 Figure Texas Instruments Incorporated 2 education.ti.com
3 c. Using the pattern observed in the previous table, if a point on the pre-image triangle has coordinates (5, 8), what are the coordinates of its corresponding point on the image triangle? That is (5, 8) means maps to Similarly, the point ( 3, 7) would map to what point? That is ( 3, 7). d. In general, if a point on the pre-image triangle has coordinates (x, y), what are the coordinates of its corresponding point on the image triangle? That is (x, y) means maps to 4. Reset the page. Press (/. ). Change the angle of rotation to 270 o. the space bar (_) to select 270 o and to close the menu. or press Q to rotate ABC 270 o about the origin. a. Record the Original coordinates (first coordinates displayed) in the first row of the following table. Look for patterns. b. Investigate and mentally make note of the coordinates by grabbing and moving each of the Record a set of data observed in row Figure 1 in the following table. Repeat and move each of the three vertices and record a set of data in row Figure 2 below. Suggestion: Move point A to Quadrant II and move point C to Quadrant IV. Look for patterns among the coordinates of corresponding vertices. Rotate 270 o A B C A B C Original Figure 1 Figure 2 c. Using the pattern observed in the previous table, if a point on the pre-image triangle has coordinates (5, 8), what are the coordinates of its corresponding point on the image triangle? That is (5, 8) means maps to 2017 Texas Instruments Incorporated 3 education.ti.com
4 Similarly, the point ( 3, 7) would map to what point? That is ( 3, 7). d. In general, if a point on the pre-image triangle has coordinates (x, y), what are the coordinates of the corresponding point on the image triangle? That is (x, y) means maps to 5. Reset the page. Press (/. ). Change the angle of rotation to 360 o. the space bar (_) to select 360 o and to close the menu. or press Q to rotate ABC 360 o about the origin. a. Discuss in your groups what you see on the screen. Investigate and mentally make note of the coordinates by grabbing and moving each of the b. Based upon your observations, to what point would (5, 8) map? That is (5, 8) c. In general, the point (x, y) would map to what point? That is (x, y). 6. Summarize the results of these investigations below: ABC is rotated about the origin. The number of degrees of rotation is given below along with the coordinates of a point, (p, q), on the pre-image ABC. Write the coordinates of the corresponding point on its image. a. ABC is rotated 90 o about the origin. (p, q) b. ABC is rotated 180 o about the origin. (p, q) c. ABC is rotated 270 o about the origin. (p, q) d. ABC is rotated 360 o about the origin. (p, q) 2017 Texas Instruments Incorporated 4 education.ti.com
5 7. Using the results from exercise 6 a d, perform the following rotations on the grid supplied. a. Rotate ABC 90 o about the origin, P. Label the vertices A, B, and C. b. Rotate ABC 180 o about the origin, P. Label the vertices A, B, and C. c. Rotate ABC 270 o about the origin, P. Label the vertices A, B, and C. List the coordinates of the points below: A: B: C: A : B : C : A : B : C : A : B : C : d. What is true about these four triangles? e. Draw APA'. What is the measure of APA' f. Draw CPC ''. What is the measure of CPC '' g. Draw BPB'''. What is the measure of BPB'''??? h. What is the image of ABC when it is rotated 360 o about the origin? 2017 Texas Instruments Incorporated 5 education.ti.com
6 8. Perform the following rotations on the grid supplied. a. Rotate DEF 90 o about the origin, P. Label the vertices D, E, and F. b. Rotate DEF 180 o about the origin, P. Label the vertices D, E, and F. c. Rotate DEF 270 o about the origin, P. Label the vertices D, E, and F. List the coordinates of the points below: D: E: F: D : E : F : D : E : F : D : E : F : d. What is true about these four triangles? e. Draw DPD '. What is the measure of DPD ' f. Draw D" PD '''. What is the measure of D" PD ''' g. Draw E ' PE '''. What is the measure of E ' PE '''??? h. What is the image of DEF when it is rotated 360 o about the origin? 2017 Texas Instruments Incorporated 6 education.ti.com
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