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Transformations & Dilations

geometry on a coordinate plane

cocoore
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Transformations & Dilations

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  1. Tuesday May 10th • Outcome/HW: • Agenda: • To Do: • Sharpen pencils • Copy Agenda • Complete the Warm-Up • Dilation Activity • Dilations- Group and Regroup Activity Students will be able to dilate geometric figures, DeltaMath #4 due by May 13th Transformation Quiz this Thursday

  2. Tuesday May 10th • Outcome/HW: • Agenda: • To Do: • Sharpen pencils • Copy Agenda • Complete the Warm-Up • Dilations- Group and Regroup Activity • DeltaMath Time Students will be able to dilate geometric figures, DeltaMath #4 due by May 13th Transformation Quiz this Friday Transformation activity from Friday due tomorrow.

  3. Dilations Dilations Dilations Dilations Dilations

  4. DILATIONS Recap!

  5. Directions: Graph the dilated image of triangle JKL using a scale factor of 2 and (0,0) as the center of dilation. MCAP Review- Circle the correct answer. The graph of the system of equations is shown on the coordinate plane. If the scale factor is 2, will it be an enlargement or reduction? ___________________ The solution is … • (2, 7) because the solution to the system must satisfy both equations simultaneously. • The solution is (1, 6) because the solution to the system must satisfy one equation or the other equation. • The solution is (3, 5) because the solution to the system must represent the y -intercepts of both equations. • The solution is ( 1.5, 5) because the solution to the system must represent the x -intercepts of both equations.

  6. Directions: Graph the dilated image of triangle JKL using a scale factor of 2 and (0,0) as the center of dilation. MCAP Review- Circle the correct answer. The graph of the system of equations is shown on the coordinate plane. Answer Key If the scale factor is 2, will it be an enlargement or reduction? ___________________ The solution is … • (2, 7) because the solution to the system must satisfy both equations simultaneously. • The solution is (1, 6) because the solution to the system must satisfy one equation or the other equation. • The solution is (3, 5) because the solution to the system must represent the y -intercepts of both equations. • The solution is ( 1.5, 5) because the solution to the system must represent the x -intercepts of both equations.

  7. Dilation Activity: Ordered pairs: L S S ( , ) A ( , ) I ( , ) L ( , ) A I

  8. Scale factor of 2 Ordered pairs: Dilation Activity: Important rule: You multiply your scale factor to both values in the ordered pair.(x,y) (x (k), y (k)) S (-1,2) A (-1,0) I (1,0) L (1,2 )

  9. Scale factor of 2 Ordered pairs: Dilation Activity: Important rule: You multiply your scale factor to both values in the ordered pair.(x,y) (x (k), y (k)) S (-1,2) x (2) = A (-1,0) x (2) = I (1,0) x (2) = L (1,2 ) x (2) =

  10. Important rule: You multiply your scale factor to both values in the ordered pair.(x,y) (x (k), y (k)) Scale factor of 2 Ordered pairs: Dilation Activity: S (-1,2) x(2), -1 2=-2 A (-1,0) x(2), -1 2=-2 I (1,0) x(2), 1 2= 2 L (1,2 ) x(2), 1 2= 2

  11. Ordered pairs: Scale factor of 2 Dilation Activity: Important rule: You multiply your scale factor to both values in the order pair.(x,y) (x (k), y (k)) S (-1,2) y(2) A (-1,0) y(2) I (1,0) y(2) L (1,2 ) y(2)

  12. Important rule: You multiply your scale factor to both values in the order pair.(x,y) (x (k), y (k)) Ordered pairs: Scale factor of 2 Dilation Activity: S (-1,2) y(2) 2 2= 4 A (-1,0) y(2) 0 2= 0 I (1,0) y(2) 0 2= 0 L (1,2 ) y(2) 2 2= 4

  13. Important rule: You multiply your scale factor to both values in the ordered pair.(x,y) (x (k), y (k)) Ordered pairs: Scale factor of 2 Dilation Activity: S (-1,2) (-2,4) A (-1,0) (-2,0) I (1,0) (2,0) L (1,2 ) (2,4)

  14. Ordered pairs: Scale factor of 2 Dilation Activity: L’ S’ L S S (-1,2) S’ (-2,4) A (-1,0) A’ (-2,0) I (1,0) I’ (2,0) L (1,2 ) L’ (2,4) A A’ I I’

  15. Let’s try another one: Ordered pairs: S U S ( , ) U ( , ) N ( , ) N

  16. Ordered pairs: Let’s try another one: S U S (-2,4 ) U ( 4,4 ) N ( 0,-2 ) N

  17. Let’s try another one: Scale factor ½ Ordered pairs: S U S (-2 x (½),4 x (½) ) U (4 x (½),4 x (½) ) N (0 x (½),-2 x (½) ) N

  18. Ordered pairs: Let’s try another one: Scale factor ½ S U S (2 x (½),4 x (½) ) =S’(-1,2) U (4 x (½),4 x (½) ) =U’(2,2) N (0 x (½),2 x (½) ) =N’(0,-1) N

  19. Dilations Dilations Dilations Group/Regroup Activity Dilations Dilations

  20. 1

  21. 1

  22. SQUARE P JBML G PA AD M

  23. Similar Figures True or False TRUE TRUE Similar Figures are the same shape and same size. Similar Figures are the same size just different shapes. Similar Figures are the same shape but different size. Similar Figures have corresponding congruent sides and corresponding congruent angles. Similar Figures have corresponding congruent angles and corresponding proportional sides. TRUE TRUE TRUE FALSE FALSE FALSE FALSE FALSE

  24. You can click on the smaller trapezoid and rotate the smaller trapezoid so that you can see the corresponding sides and angles better!

  25. G H I J K L

  26. Notes - Transformation Rules Dilations Rule: To dilate a point, multiply both the x-coordinate and y-coordinate by the scale factor. (rx,ry) Examples: Dilate each using a scale factor of 3 (enlargement). Pre-image: (6,8)..... Image (18,24) Pre-image: (-7,0)..... Image (-21,0) Pre-image: (0,-5)..... Image (0,-15) Pre-image: (-10,10)..... Image (-30,30)

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