Math 8C Unit 8 – Day 4

1. Math 8CUnit 8 – Day 4 Standards: (A): Use transformations to move objects on the coordinate plane and show two figures are congruent or similar. (B): Define rotation, reflection, and translation in terms of angles, arcs, parallel and perpendicular lines.

2. (5x-4)o

3. Transformations A transformation is a change in position, shape, or size of a figure.

4. Four Types of Transformations • Translation: When a figure is shifted, or moved a certain distance in a certain direction. • Reflection: When a figure is reflected, or flipped across a certain line, its image is reversed and equidistant to the line of reflection. • Rotation: When a figure is rotated a certain angle around a certain point. • Dilation: When a figure expands or shrinks in size by a constant number called a scale factor.

5. Congruent or Similar? • Congruent: Two objects are congruent if they have the same shape and the same size. • Similar: Two objects are similar if they have the same shape, and proportional sizes.

6. Translations  A translation is a transformation that moves all points of a figure the samedistancein the same direction. • Example: Translate the figure two units up, and three units left.

7. You Try!! • Translate the figure three units right andfour units down.

8. You Try • Translate the figure 2 units to the right,and three units down. • Do translationsproduce congruentfigures or similar figures? • Congruent. Same shape, same size.

9. Reflections A reflection is when an image is flipped over a certain line. Its reflection is a mirror image, equidistant from the reflection line. • Images will be reflected: • About the -axis • About the -axis

10. Reflections About the -Axis • How are the coordinates changing? • Rule:

11. Example – You Try! • Reflect this image about the -axis. • Are these figurescongruent or similar? • Congruent. Same shape,same size.

12. Reflections About the -Axis • How are the coordinates changing? • Rule:

13. Example – You Try! • Reflect the figure about the -axis. • Reflections produce congruentfigures!

14. Rotations In order to rotate an object you must know: • The center of the rotation, usually the origin. • The angle of the rotation; 90° or 180° • The direction of the rotation.

15. Rotating Clockwise 90° Notice how the coordinates of point P change • What do you notice about the points on the flag PGRS as it is rotated? In general:

16. Rotating Clockwise 90° Example • Rotate the figure Clockwise 90°

17. Rotating Counter-Clockwise 90° Notice how the coordinates of point B change • What do you notice about the points on the rectangle ABCD? In general:

18. Rotating Clockwise 180° Notice how the coordinates of point (2, 2) change • What do you notice about the points on the figure? All coordinates change sign. In general:

19. You Try!! • Rotate the image 90° clockwise • Now rotate the originalimage 180° • Congruent or similar? • Congruent: Same shape, same size.

20. Rules for Rotations • Clockwise 90° : • Counter-Clockwise 90° : • 180° :

21. Dilations • Dilation: When a figure expands or shrinks in size by a constant number called a scale factor. • What pattern do you notice withthe coordinates? • From E to A to K, their valuesdouble every time. • From M to C to G, their valuesare halved each time. • Is this the same pattern forall the points?

22. Dilations • To dilate a figure, we multiplyeach coordinate by a number calleda scale factor, k. • If the scale factor is larger than 1, thefigure will grow. • If the scale factor is smaller than 1, thefigure will shrink. • Rule:

23. Example • Dilate the figure by a factor of 3. • Are these figures congruent orsimilar? • Similar (same shape, differentsize). • Rule: Dilations produce similarfigures, not congruent figures.

24. Example • Determine the scale factor, k, from the dilation shown. • , if dilating figure ABCD • Or , if dilating figure EFHG

25. You Try! • Perform the following transformations on figure ABCD.

26. In Class Practice U8D4 - ICP