Warm-up Begin at the word “A.” Every time you move, write down the word(s) upon which you land. heart dream a 1. Move to the consecutive interior angle. 2. Move to the alternate interior angle. makes 3. Move to the corresponding. A 4. Move to the alternate exterior. 5. Move to the exterior linear pair. wish is 6. Move to the alternate exterior angle. your 7. Move to the vertical angle.
RIGID TRANSFORMATIONS The preimage and image are congruent. Geometry in Motion RIGID TRANSFORMATIONS The preimage and image are congruent. * Translations * Reflections * Rotations
* Translations (Slide your image over) * image * preimage
* Reflections (Flip your image over) * preimage * image
(Turn your image about a fixed point ) * Rotations (Turn your image about a fixed point ) * image * preimage
What are the different transformations?
Translating slides the object up, down, left, right.
Translation (slide) (x,y)(x – 2, y + 2) B C A Move left 2 then up 2
(x,y)(x +5, y ) E Move right 5 G F
Reflect over the x-axis Reflect over the y-axis Reflections Reflect over the x-axis Reflect over the y-axis
Reflecting across the x-axis… changes the sign of the
Reflect over the x-axis Change the sign of the y
Example: Reflect over the x-axis 3 -1 -2 -3 -3 3 1 4
Reflect over the x-axis
Reflect over the x-axis
Reflect over the x-axis
Reflecting across the y-axis… changes the sign of the
Reflect over the y-axis Change the sign of the x
Example: Reflect over the y-axis -2 4 1 8 4 -4 -2 -5
Reflect over the y-axis
Reflect over the y-axis
Reflect over the y-axis
Reflect over the y-axis Odd Shapes Reflect over the y-axis
Rotations
Rotation is simply turning about a fixed point. For our purposes, the fixed point will be the origin Rotate 90 counterclockwise about the origin Rotate 180 about the origin Rotate 90clockwise about the origin
CLOCKWISE is a right turn.
Hands in the air on the wheel. Left hand is x Right hand is y
Which hand is at 12 o’clock first? Make a clockwise turn. Which hand is at 12 o’clock first? X
Rotate 90 degrees clockwise. Change the sign of x & switch the order of x and y.
Example: Rotate 90 degrees clockwise.
Rotate 90° clockwise 3 7 4 -1 1 -3
Rotate 90° clockwise
COUNTERCLOCKWISE is a left turn.
Hands in the air on the wheel. Left hand is x Right hand is y
Make a counterclockwise turn. Which hand is at 12 o’clock first? Y
Rotate 90 degrees counterclockwise. Change the sign of y & Switch the order of x and y
Example: Rotate 90 degrees counterclockwise.
Rotate 90° counterclockwise
Rotate 90° counterclockwise
Rotating 180 degrees changes the sign of the x and the sign of the y.
change the sign of both x & y. Rotate 180 degrees. Keep the order & change the sign of both x & y.
Example: Rotate 180 degrees.
Rotate 180°
Rotate 180°
The image and preimage are similar. Dilations REDUCTIONS ENLARGEMENTS Your image is smaller than your original Your image is larger than your original Scale Factor is a fraction between zero and one Scale Factor is a number bigger than one The image and preimage are similar. Dilations are not a rigid transformation.
All you do is multiply k to (x, y). Find the coordinates of the dilation image for the given scale factor, k. Example 1: G(0, -2), H(1, 3), and I(4, 1); k = 2 All you do is multiply k to (x, y). G’( , ), H’( , ), and I’( , )
All you do is multiply k to (x, y). Find the coordinates of the dilation image for the given scale factor, k. Example 2: L(8, -8), N(0, 16), and M(4, 5); k = 1/4 All you do is multiply k to (x, y). L’( , ), N’( , ), and M’( , )
k = 1/2
k = 2
Practice Does the Brain Good. Translations, Reflections, Rotations & Dilations Practice Practice Finish
Warm-up Begin at the word “A”. Every time you move, write down the word(s) upon which you land. heart dream a 1. Move to the consecutive interior angle. 2. Move to the alternate interior angle. makes 3. Move to the corresponding. A 4. Move to the alternate exterior. 5. Move to the exterior linear pair. wish is 6. Move to the alternate exterior angle. your 7. Move to the vertical angle.
______ TRANSFORMATIONS The preimage and image are _________. Geometry in Motion ______ TRANSFORMATIONS The preimage and image are _________. * Translations * Reflections * Rotations
* Translations (____ your image over) * image * preimage
* Reflections (____ your image over) * preimage * image
(____ your image about a fixed point) * Rotations (____ your image about a fixed point) * image * preimage
What are the different transformations?
Translating slides the object up, down, left, right.
Translation (slide) (x,y)(x – 2, y + 2) B C A
(x,y)(x +5, y ) E G F
Reflect over the x-axis Reflect over the y-axis Reflections Reflect over the x-axis Reflect over the y-axis
Reflect over the x-axis Change the sign of the y
Example: Reflect over the x-axis
Reflect over the x-axis
Reflect over the x-axis
Reflect over the x-axis
Reflect over the y-axis Change the sign of the x
Example: Reflect over the y-axis
Reflect over the y-axis
Reflect over the y-axis
Reflect over the y-axis
Reflect over the y-axis Odd Shapes Reflect over the y-axis
Rotations
Rotation is simply turning about a fixed point (the origin). Rotate 90 counterclockwise about the origin Rotation is simply turning about a fixed point (the origin). Rotate 90clockwise about the origin Rotate 180 about the origin
CLOCKWISE is a ______ turn.
Rotate 90 degrees clockwise. Change the sign of x & switch the order of x and y.
Example: Rotate 90 degrees clockwise.
Rotate 90° clockwise
Rotate 90° clockwise
COUNTERCLOCKWISE is a ______ turn.
Rotate 90 degrees counterclockwise. Change the sign of y & Switch the order of x and y
Example: Rotate 90 degrees counterclockwise.
Rotate 90° counterclockwise
Rotate 90° counterclockwise
change the sign of both x & y. Rotate 180 degrees. Keep the order & change the sign of both x & y.
Example: Rotate 180 degrees.
Rotate 180°
Rotate 180°
The image and preimage are ______. Dilations REDUCTIONS ENLARGEMENTS Your image is smaller than your original Your image is larger than your original Scale Factor is a fraction between zero and one Scale Factor is a number bigger than one The image and preimage are ______. Dilations are ____ a ______ transformation.
All you do is multiply k to (x, y). Find the coordinates of the dilation image for the given scale factor, k. Example 1: G(0, -2), H(1, 3), and I(4, 1); k = 2 All you do is multiply k to (x, y). G’( , ), H’( , ), and I’( , )
All you do is multiply k to (x, y). Find the coordinates of the dilation image for the given scale factor, k. Example 2: L(8, -8), N(0, 16), and M(4, 5); k = 1/4 All you do is multiply k to (x, y). L’( , ), N’( , ), and M’( , )
k = 1/2
k = 2
Practice Does the Brain Good. Translations, Reflections, Rotations & Dilations Practice Practice Finish