1. Sept 10, 2013
Transformations
Unit 1Review

2. Warm Up # 1
Alicia says the quadrilaterals below must be congruent because their angles are congruent
Is she correct? Explain why or why not?

3. Warm Up #2

4. Types of Transformations
Reflections: These are like mirror images as seen across a line or a point.
Translations ( or slides): This moves the figure to a new location with no change to the looks of the figure.
Rotations: This turns the figure clockwise or counter-clockwise but doesn’t change the figure.
Dilations: This reduces or enlarges the figure to a similar figure.
Lesson 10-5: Transformations

5. Lesson 10-5: Transformations
Reflections
You can reflect a figure using a line or a point. All measures (lines and angles) are preserved but in a mirror image.
Example:
The figure is reflected across line l . l
You could fold the picture along line l and the left figure would coincide with the corresponding parts of right figure.
Lesson 10-5: Transformations

6. Reflections – continued…
Reflection across the x-axis: the x values stay the same and the y values change sign (x , y)  (x, -y)
Reflection across the y-axis: the y values stay the same and the x values change sign (x , y)  (-x, y)
Example:
In this figure, line l : n l
reflects across the y axis to line n
(2, 1)  (-2, 1) & (5, 4)  (-5, 4)
reflects across the x axis to line m.
(2, 1)  (2, -1) & (5, 4)  (5, -4) m
Lesson 10-5: Transformations

7. Translations (slides)
If a figure is simply moved to another location without change to its shape or direction, it is called a translation (or slide).
If a point is moved “a” units to the right and “b” units up, then the translated point will be at (x + a, y + b).
If a point is moved “a” units to the left and “b” units down, then the translated point will be at (x - a, y - b).
Example: A
Image A translates to image B by moving to the right 3 units and down 8 units. B
A (2, 5)  B (2+3, 5-8)  B (5, -3)
Lesson 10-5: Transformations

8. Composite Reflections
If an image is reflected over a line and then that image is reflected over a parallel line (called a composite reflection), it results in a translation.
Example: C B A
Image A reflects to image B, which then reflects to image C. Image C is a translation of image A
Lesson 10-5: Transformations

9. Lesson 10-5: Transformations
Rotations
An image can be rotated about a fixed point.
The blades of a fan rotate about a fixed point.
An image can be rotated over two intersecting lines by using composite reflections.
Image A reflects over line m to B, image B reflects over line n to C. Image C is a rotation of image A. A B C m n
Lesson 10-5: Transformations

10. Lesson 10-5: Transformations
Rotations
It is a type of transformation where the object is rotated around a fixed point called the point of rotation.
When a figure is rotated 90° counterclockwise about the origin, switch each coordinate and change the sign of y coordinate.
(x, y) (-y, x)
Ex: (1,2) (-2,1) & (6,2)  (-2, 6)
When a figure is rotated 180° about the origin, change signs of both coordinates.
(x, y) (-x, -y)
Ex: (1,2) (-1,-2) & (6,2)  (-6, -2)
Lesson 10-5: Transformations

11. Lesson 10-5: Transformations
Dilations
A dilation is a transformation which changes the size of a figure but not its shape. This is called a similarity transformation.
Since a dilation changes figures proportionately, it has a scale factor k.
If k is greater than 1, the dilation is an enlargement.
If k is between 0 and 1, the dilation is a reduction.
If k is equal to 1, the dilation is congruence transformation. (No size change occurs.)
Lesson 10-5: Transformations