Transformations
What type of transformation is shown?
(x,y)---(x+6, y-4)
Translation
What is the composition of transformations?
ABCD rotated 180 degrees and dilated by a factor of 1/3.
(x,y)---(-x,-y)---(-1/3x, -1/3y)
A(2,4), B(9,4), C(12,-2), D(-3, -4) dilated by a factor of 2. Graph the image and preimage. Label points.
A'(4,8), B'(18,8), C'(24,-4), D'(-6, -8)
What type of transformation is shown?
(x,y)---(8x, 8y)
Dilation
LMNO is translated right 5 units and up 3 units, rotated counterclockwise 90 degrees, and dilated by a factor of 1/2.
(x,y)---(x+5, y+3)---(-(y+3), x+5)---
(-1/2(y+3), 1/2(x+5)
What type of transformation is shown?
(x,y)---(1/2x, y)
Horizontal Compression
A dilation changes the x, y or both?
Apply the composition of transformation to triangle ABC with vertices A(-2,8), B(2,4), and C(-2,6). Write the coordinates of the image and graph the image and preimage. Label points.
(x,y)---(-1/2x + 3, -1/2y + 3)
A'(4,-1), B'(2,1), C'(4,0)
HIJ is dilated by a factor of 4, reflected over the y-axis, and translated right 3 units and up 5 units. What is the composition of transformation?
Use this composition to find the image given the vertices H(1,1), I(1,-1), and J(-2,3)
Composition: (-4x-12, 4y+20)
H'(-16,24), I'(-16,16), and J'(-4,32)
What type of transformation is shown?
(x,y)---(x, 9y)
Vertical Stretch
What is the k factor of the image to the preimage?
3/4
What is the difference between a horizonal stretch/compression and a vertical stretch/compression?
Stretch k>1
Compression 0<k<1
Horizontal--only changes the x
Vertical---only changes the y
What is the k factor of the image to the preimage?
5/4
Apply the composition of transformation to triangle ABC with vertices A(-4,-2), B(0,3), and C(-4,3). Write the coordinates of the image and graph the image and preimage. Label points.
(x,y)---(-4y - 2, 4x - 2)
A'(6, -18), B'(-14,-2), and C'(-14,-18)