Composite Transformations Geometry

1. Monday May 23rd

2. Name- ____________________________ Warm-Up 3. Dilate with a scale factor of 2. • Figure W is the result of a transformation on Figure V. Which transformation would accomplish this? 2. Figure G is the result of a transformation on Figure F. Which transformation would accomplish this? H (___,___) D (___,___) V (___,___) preimage image H’ (___,___) D’ (___,___) V’ (___,___)

3. Name- ____________________________ Warm-Up 3. Dilate with a scale factor of 2. • Figure W is the result of a transformation on Figure V. Which transformation would accomplish this? 2. Figure G is the result of a transformation on Figure F. Which transformation would accomplish this?

4. Identify 2 images that are congruent. How can you prove it?

5. A & D • Translate right 1, down 5 & reflect over the y-axis • A & E • Translate right 4 & reflect over the x-axis • A & G • Reflect over the x-axis & y-axis Any others?

6. We Do Practice

7. We Do Practice

8. You Do Practice

9. You Do Practice

10. Teachers click here for link.

11. Let’s try a multi-step transformation together. The Quadrilateral JKLM has coordinates J(2,-1),K(1,2),L(1,-3) and M(3,-2). Graph J”K”L”M”, the image of JKLM with a scale factor (k) of 3 and a reflection across the y-axis.

12. What is the first translation that is being asked for? The Quadrilateral JKLM has coordinates J(2,-1),K(1,2),L(1,-3) and M(3,-2). Graph J”K”L”M”, the image of JKLM with a scale factor (k) of 3 and a reflection across the y-axis.

13. What is the first translation that is being asked? The Quadrilateral JKLM has coordinates J(2,-1),K(1,2),L(1,-3) and M(3,-2). Graph J”K”L”M”, the image of JKLM with a scale factor (k) of 3 and a reflections across the y-axis.

14. Graph JKLM, the image of J’K’L’M’ with a scale factor (k) of 3. Dilation of 3: J(2,-1) J’( , ) K(1,-2) K’( , ) L(1,-3) L’( , ) M(3,-2) M’( , )

15. Graph JKLM, the image of JKLM with a scale factor (k) 3. Dilation of 3: J(2,-1) J’(6 ,-3 ) K(1,-2) K’(3 ,-6 ) L(1,-3) L’(3 ,-9 ) M(3,-2) M’(9 ,-6 ) Dilation means multiply each value by the scale factor (3) in this problem. (x’,y’) = (x(3), y(3))

16. Is K’J’M’L’ similar to KJML?

17. Is K’J’M’L’ similar to KJML? • Yes, • same shape • same angle measurements

18. How is K’J’M’L’ different than KJML?

19. How is K’J’M’L’ different than KJML? • Different • side measurements • enlarged by scale factor of 3.

20. What is the second translation that is being asked for? The Quadrilateral JKLM has coordinates J(2,-1),K(1,2),L(1,-3) and M(3,-2). Graph J”K”L”M”, the image of JKLM with a scale factor (k) of 3 and a reflection across the y-axis.

21. Now graph J’K’L’M’, over the y-axis. Reflection across y-axis: J(2,-1) J’(6 ,-3 ) J”( , ) K(1,-2) K’(3 ,-6 ) K”( , ) L(1,-3) L’(3 ,-9 ) L”( , ) M(3,-2) M’(9 ,-6 ) M”( , )

22. Now graph J’K’L’M’, over the y-axis. Reflection across y-axis: J(2,-1) J’(6 ,-3) J”(-6,-3) K(1,-2) K’(3 ,-6) K”(-3,-6) L(1,-3) L’(3 ,-9) L”(-3,-9) M(3,-2) M’(9 ,-6) M”(-9,-6) Reflection means opposite x values but keep y-values. (x,y) = (-x,y)

23. Is K’J’M’L’ similar to K”J”M”L”?

24. Is K’J’M’L’ similar to K”J”M”L”? Yes, Same angle measurements Same side measurements Therefore, they are congruent.

25. Now you try!

26. Plot the points that are given A( -2,1),B(-4,2) & C(-1,4) Dilate the ABC image by a scale of 3. A’( , ) B’ ( , ) C’( , ) Reflect over the x-axis A” ( , ) B” ( , ) C”( , )

27. Is ABCD similar to EFGH?

28. Is ABCD similar to EFGH? Yes, ABCD~EFGH because a rotation of 180o. Then you would use dilation with a scale factor of 0.5.

29. What must I do first to move the trapezoid?

31. What must I do first to move the trapezoid?

32. Reflection

33. One possible sequence, is to reflect ABCD across the x-axis. A’B’C’D’.

34. Notice that trapezoid A’B’C’D’ is similar to GKJH, just smaller. What transformation did we learn that could make the shape smaller?

35. ADilation is the transformation that will reduce the size of the trapezoid.