Transformation Review
Parallelogram ABCD is rotated 90 degrees clockwise around the origin. How many parallel sides does the image A'B'C'D' have?
2 pairs
What is the mapping notation for a dilation with scale factor 1.5 centered at the origin?
(x,y)→(kx,ky)
The rectangle STUV undergoes a dilation of scale factor 3 centered at (0,0) to produce the image S'T'U'V'. If ∠V is 60 degrees, what is the measure of ∠V'?
60 degrees
What is the mapping notation for a dilation centered at the origin with a scale factor of 1/2, followed by a translation right 6 units and down 3 units?
(x,y)→((1/2 x)+6, (1/2 y)-3)
A figure is dilated by a scale factor of 3. Which statement about the figure and its image is true?
A: They are congruent. The perimeters and areas are equal.
B: They are similar. The perimeter and area of the original figure are tripled.
C: They are similar. The perimeter of the original figure is multiplied by 3, and the area is multiplied by 9.
D: They are different shapes and sizes. The perimeter of the original figure is multiplied by 9, and the area is multiplied by 3.
C
Triangle JKL is rotated 90 degrees counterclockwise, then translated right 2 units and down 7 units; this series of transformations form the image J'K'L'. The ∠L must have the same measure as which angle?
∠L'
Triangle WYZ, where point W is located at (2,9), undergoes a dilation centered at (0,0) to produce the image W'Y'Z', with point W' at (5,22.5). What is the scale factor of the dilation?
2.5
Triangle MNO has side lengths of 24 ft, 48 ft, and 32 ft. Which side lengths could belong to a dilation of triangle MNO?
A: 3 ft, 6 ft, 4 ft
B: 6 ft, 12 ft, 9 ft
C: 34 ft, 58 ft, 42 ft
D: 48 ft, 98 ft, 64 ft
A
See Image
D
Jenya obtained the image of △ABC after a dilation with a scale factor of 3. The area of △ABC is 7 square centimeters, and its perimeter is 20 centimeters. What is the area and perimeter of the image △A'B'C'?
Area: 63 square centimeters
Perimeter: 60 centimeters
The point (11,-8) is translated right 4 units, then reflected over the x-axis. What are the coordinates of its image?
(15,8)
The line segment AD has a length of 8. Trapezoid ABCD is dilated by a scale factor of 3/8, with the dilation centered at the origin; this dilation creates the image A'B'C'D'. What is the length of the line segment A'D'?
3
The triangle ABC is such that AB/BC = 1/6. Triangle ABC is then dilated by a scale factor of 2 to form the image A'B'C'. What is A'B'/B'C'?
1/6
The point (−2, −3) is rotated 180° about the origin, then dilated with a center of (0,0) and a scale factor of 4. What are the coordinates of the resulting image?
(8,12)
A figure graphed on a coordinate plane is reflected across the y-axis, then translated 4 units to the left and 10 units down. What is the mapping notation for this series of transformations?
A triangle has vertices at (0,0), (4,0), and (4,2). The triangle is then rotated 90 degrees counterclockwise around the origin, then reflected across the y-axis. What are the vertices of the triangle's image?
(0,0), (0,4), and (2,4)
The line GH has a length of 6. The square EFGH undergoes a dilation centered at (0,0) with a scale factor of 4.5; the image of EFGH is E'F'G'H. What is the length of the line segment E'F'?
27
Triangle XYZ undergoes a transformation with the mapping notation (x,y)→(7x,7y). Fill in the blanks:
1. The preimage and image are _________ to each other.
2. The area the image X'Y'Z', is ________ times the area of XYZ.
3. The perimeter the image X'Y'Z', is ________ times the perimeter of XYZ.
1. Similar
2. 49 times
3. 7 times
See Image
A reflection across a vertical line followed by a dilation with a scale factor of 5.
In triangle XYZ, the measure of ∠X = 37 degrees, and the measure of ∠Y = 88 degrees. If triangle X'Y'Z' is the image of triangle XYZ after a translation of 8 inches and a rotation of 90 degrees counterclockwise, what is the measure of ∠Z' ?
55 degrees
What is the mapping notation for a 2,970 degree clockwise rotation?
(x,y)→(y,-x)
Write an inequality to represent the possible values of a scale factor, k, of a reduction.
0<k<1 or k<1
The square CDEF is rotated 90 degrees clockwise around the origin, then translated 5 units down; its image is C'D'E'F'. Another square, MNOP is dilated by a scale factor of 2 centered at (0,0). Its image is M'N'O'P'. Are C'D'E'F' and M'N'O'P' congruent? Are they similar?
What is the mapping notation for a 90 degree counterclockwise rotation, followed by a dilation of scale factor 71 centered at (0,0), followed by a reflection across the x-axis?
(x,y)→(-71y,-71x)
Point J is located at (0,0), Point K is located at (6,0), and Point L is located at (0,6). The equilateral triangle JKL undergoes a dilation centered at (0,0) with a scale factor of 2/3; the image of JKL is J'K'L'. What is the area of J'K'L'?
8 units2