Translation
A translation along vector <2,1> means what?
2 units right, 1 unit up. (x+2, y+1)
What are the three pieces of information needed in order to complete a rotation?
Direction, center of rotation, angle of roation.
Complete these:
Reflection across x-axis: (x,y) --> (?,?)
Reflection across y-axis: (x,y) --> (?,?)
Reflection across line y=x: (x,y) --> (?,?)
Reflection across x-axis: (x,y) --> (x,-y)
Reflection across y-axis: (x,y) --> (-x,y)
Reflection across line y=x: (x,y) --> (y,x)
Give the most complete definition of dilation you can.
Dilation is a similarity transformation that enlarges or reduces a figure proportionally. Dilations are completed with respect to a center point and a scale factor.
Two reflections are done over parallel lines 5 inches apart. What single transformation could have produced the same result?
Translation 10 inches.
Trianle ABC has coordinates A(3,7)B(4,1)C(8,-3). The triangle is translated along vector <-5,4>. What are the coordinates of C'?
C'(3,1)
Trianle ABC has coordinates A(3,7)B(4,1)C(8,-3). The triangle is rotated 90º about the origin. What are the coordinates of A'?
A'(-7,3)
What are the coordinates of point G(4,-9) after a reflection over the x-axis?
G'(4,9)
A dilation with scale factor 0.5 indicates that the dilation will be a ____________
Reduction
Reflections are done over two lines that intersect at an angle of 40º. What single transformation would produce the same result?
Rotation 80º.
Trianle ABC has coordinates A(3,7)B(4,1)C(8,-3). B' is located at coordinates (-4,-1). What is the translation vector?
<-8,-2>
Trianle ABC has coordinates A(-3,2)B(-1,12)C(5,-3). The triangle is rotated 180º. What are the coordinates of B'?
B'(1,-12)
Point R(-5,2) is reflected across the line y=x, then across the y-axis. What are its new coordinates?
R'(-2,-5)
A dilation is completed on a triangle with coordinates B(4,2)I(-1,8)G(3,-1). The scale factor of the dilation is 2. The center of dilation is the origin. What are the coordinates of I'?
I'(-2,16)
A regular polygon has rotational symmetry order 6 and a magnitude of 60º. What is the figure?
Hexagon
Trianle ABC has coordinates A(3,7)B(4,1)C(8,-3). After a translation, A' is located at (-2,-1). What are the coordinates of C'?
C'(3,-11)
Trianle ABC has coordinates A(-3,2)B(-1,12)C(5,-3). The triangle is rotated 270º clockwise about the origin. What are the coordinates of C'?
C'(3,5)
Triangle GHJ with coordinates G(3,5)H(-1,2)J(-4,-2) is reflected over the y-axis. What are the coordinates of G'H'J'?
G'(-3,5)
H'(1,2)
J'(4,-2)
Triangle R'(-10,-8)S'(-6,12)T'(18,-6)
Triangle R(-5,-4)S(-3,6)T(9,-3)
What is the scale factor?
How many lines of symmetry can you draw in a square?
4
Trianle ABC has coordinates A(3,7)B(4,1)C(8,-3). The triangle is translated along vector <-2,6>, then along the vector <-6,-12>. What are the coordinates of triangle A'B'C'?
A'(-5,1)
B'(-4,-5)
C'(0,-9)
Trianle ABC has coordinates A(-3,2)B(-1,12)C(5,-3). The triangle is rotated 270º. What are the coordinates of A'B'C'?
A'(2,3)
B'(12,1)
C'(-3,-5)
Triangle XYZ with coordinates X(-9,2)Y(3,-1)Z(-3,-5) is reflected three times. Over the y-axis, then the line y=x, then the x-axis. What are its new coordinates?
X'(2,-9)
Y'(-1,3)
Z'(-5,-3)
A dilation of scale factor 1/3 is completed on point B(-9,12), then the image of that point is reflected over the x-axis. What are the coordinates of B''?
B''(-3,-4)
How many axes of symmetry does a cube have?
13