Definitions
Translations
Reflections
Dilations
Rotations
Position, Orientation and Congruency
100
A transformation in which a mirror image of a figure is produced by flipping a figure over a line.
What is a reflection?
100
Point A (12, -19) is translated twelve units to the left, and twelve units up. What are the coordinates of A'?
A' (0, -7)
100
Identify the line of reflection.
Line of Reflection: x=0
100
One of the two methods for creating a dilated image, it is most effective for images that have a point on the origin, and follows the following steps:
1. Determine the pre-image's dimensions.
2. Apply the scale factor to the dimensions by multiplying.
3. Draw the new image.
What is Method A: Using Dimensions?
100
A point that started in quadrant 4 and was rotated 270 degrees counter-clockwise would end in which quadrant?
Quadrant 3.
100
True or False:
A shape will only change its orientation under a transformation if it is rotated.
False.
Shapes also change their orientation when transformed in a reflection.
200
A transformation in which a figure is shifted up, down, left or right.
What is a translation?
200
Describe the translation below.
The image was translated Right 9 units to the right, and 9 units up.
(x,y) -> (x+9, x+9)
200
Reflect the point over the line y= -3
(0, 4)
Reflected point: (0, -10)
200
What is the scale factor of the dilation?
The scale factor of the dilation is 1/4.
200
Which point best represents the new coordinates?
Point B
200
A sequence of transformations is described below:
1. A translation.
2. A reflection over the x axis.
3. A reflection over the y axis.
Are the two shapes congruent, similar, or neither?
Has the orientation changed?
Has the position changed?
The new shape is congruent, has a new orientation and a new position.
300
A transformation which changes the size of the figure, but not the shape.
What is a dilation?
300
What is the notation for the translation that changes point Z (8,450, -2) to point Z' (-4, 10).
(x, y) -> (x-8,454, y+12)
300
Identify the line of reflection.
Line of Reflection:
y=x
300
Pentagon A'B'C'D'E is the image of the pentagon ABCDE under a dilation with a scale factor of 1/2. What is the length of segment C'D'?
2 units
300
Point P rotated by -90 degrees is best represented by Point A.
300
A sequence of transformations is described below:
1. A rotation about a point P of 180 degrees.
2. A translation of (x+1, y-1)
3. A rotation of 180 degrees.
Are the two shapes congruent, similar, or neither?
Has the orientation changed?
Has the position changed?
The new shape is congruent, with the same orientation and a new position.
400
A transformation which turns a point or figure about a fixed point, often the origin.
What is a rotation?
400
If point S (-16, 14) is translated (x,y) -> (x + 26, y - 24), what quadrant does it end up in?
It began in Quadrant 2, and was translated down to Quadrant 4.
400
Identify the line of reflection.
Line of Reflection
y= -x
400
Pentagon A'B'C'D'E is the image of the pentagon ABCDE under a dilation with a scale factor of 3/2. What is the length of segment AE?
The length of segment AE is 4 units.
Segment A'E' = 6 units
Segment AE= 6*(2/3) = 4 units
400
~105 degrees (+/- 20 degrees)
400
A sequence of transformations is described below.
1. A translation (x+2, y-3).
2. A dilation with a scale factor of .5 about a point P.
3. Another translation of (x+7, y+9)
4. A rotation of -75 degrees around the point P.
Are the two shapes congruent, similar, or neither?
Has the orientation changed?
Has the position changed?
The new shape is similar, in a new orientation with a new position.
500
A series of transformations on a figure or a point.
What is a composition of transformations?
500
What is the notation for the translation that changes point A (107, -65) to point A' (24, 19).
(x,y) -> (x-83, y+84)
500
Reflect the following points over the line x= -5.
H (-10,-2)
E (-9,2)
Y (-7,0)
New points H' (-3,0)
E' (-1,2)
Y' (0,-2)
500
Find the coordinates of the image CIAO under a dilation of 1/3.
The coordinates of the image CIAO under a dilation of 1/3 are:
C' (1,1)
I' (2,0)
A' (2, 3)
O' (4, 1)
500
Blue Triangle POT has been rotated -180 degrees around the origin. What are the new coordinates for the image P'O'T'?
P' (2, -5)
O' (2, 5)
T' (-6, 0)
500
A sequence of transformations is described below:
1. A dilation about a point P.
2. A rotation of -165 degrees about point P.
3. A horizontal stretch about a vertical line QR.
Are the two shapes congruent, similar, or neither?
Has the orientation changed?
Has the position changed?
The new shape is not similar, has a new orientation and a new position.