Translations
What is a translation?
Moving a figure on a graph.
(Left<-->Right or Up<-->down)
What happens to an image when the scale factor is greater than 1? Less than 1?
Greater than 1: image gets larger
less than 1: image gets smaller
What is a rotation?
A "turn" around the origin
What is a reflection?
A "flip" over a specified line (axis of reflection)
What is a composite transformation?
What is the algebraic rule for translations?
(x,y) --> (x+a,y+b)
What is the algebraic rule for a dilation?
(x,y) --> (kx, ky)
k = scale factor
Write the 3 main rotation rules
90º C/270º CC
(x,y) --> (y, -x)
180º C or CC
(x,y) --> (-x, -y)
270º C / 90º CC
(x,y) --> (-y, x)
A(3, -1) is reflected over the line y = x.
What is A’ ?
A'(-1,3)
(x,y) --> (y,x)
Point A(1,-3) is is translated by (x,y) → (x-4, y+3) and a reflection over the x-axis.
What are the coordinates of A’' ?
A'(-3,0)
A''(-3,0)
Write the RULE for translating a figure 5 units right and 9 units down?
(x,y) --> (x+5, y-9)
Write the rule for dilating a pre-image by a scale factor of 3.
(x,y) --> (3x, 3y)
B(-3, 2) → B’ (2, 3). Describe the rotation.
90ºC/270ºCC
(x,y) -->(y, -x)
What are the four main reflection rules?
x-axis
(x,y)-->(x,-y)
y-axis
(x,y)-->(-x,y)
y=x
(x,y)-->(y,x)
y=-x
(x,y)-->(-y,-x)
Point A(2,4) is is translated by (x,y) → (x-2, y+4) and a rotation 180º counterclockwise.
What are the coordinates of A’'?
A'(0,8)
A''(0,-8)
What is the image coordinate of the point Z(4, -2) after translating 2 units left and 3 units down?
Z'(2, -5)
4 - 2 = 2
-2 - 3 = -5
Given the point, A(-4,10) what is the new coordinate after a dilation by 1/2.
A'(-2,5)
Given ▵ABC has coordinates of A (3,1), B(-4,2), and C (10,2). What would the point B' be if it was rotated 180 degrees clockwise.
B'(4,-2)
(x,y) --> (-x,-y)
Given ▵ABC has vertices at A(3,4), B(-1,-5), and C(6,-2), what are the coordinates of the image after a reflection over the y-axis.
A'(-3,4)
B'(1,-5)
C'(-6,-2)
Point Z(-1,9) is is reflected over y= -x and then rotated 270º counterclockwise about the origin.
What are the coordinates of Z’ ?
Z'(-9,1)
Z"(1,9)
Given ▵ABC has vertices at A(4,2), B(-2,-3), and C(-3, 5), what are the coordinates of the triangle after a translation of 1 unit right and 3 units down. Write the RULE and the new POINTS.
(x,y) --> (x+1, y-3)
A'(5, -1)
B'(-1, -6)
C'(-2, 2)
Given ▵ABC has vertices at A(4,-2), B(-12,-4), and C(8, 8), what are the coordinates of the triangle after a dilation of a scale factor of 1/4? Write the RULE and POINTS!!
(x,y) --> (1/4x , 1/4y)
A'(1, -1/2)
B'(-3, -1)
C'(2,2)
Given ▵ABC has coordinates of A (1,2), B(-3, -4), and C (4, -2), rotate the figure 270 degrees clockwise.
A'(-2,1)
B'(4,-3)
C'(2,4)
(x,y)-->(-y,x)
Given ▵ABC has vertices at A(0,1), B(-2,4), and C(-2,-3), what are the coordinates of the image after a reflection over the y = -x.
WRITE THE RULE AND THE POINTS
A'(-1,0)
B'(-4,2)
C'(3,2)
(x,y)--> (-y,-x)
Given ▵ABC has coordinates of A(-2,3), B(-4, 2), and C (-1,-1), dilate the figure by 2, then rotate the figure 90º clockwise about the origin. What are the coordinates of the new figure?
A'(-4,6) B'(-8,4) C'(-2,-2)
A''(6,4) B''(4,8) C''(-2,2)