Translations
What is the vector used to translate the preimage A(-3, 2) to the image A'(0,4)
<3,2>
For a regular octagon, list all possible rotations that are less than or equal to 360 degrees that maps the polygon onto itself.
45°, 90°, 135°, 180°, 225°, 270°, 315°, and 360°
A(-1, -5), B(-2, -3), C(4, -2), D(5, -4) across the line y = −x. What are the coordinates of the image of ABCD?
A'(5, 1)
B'(3, 2)
C'(2, -4)
D'(4, -5)
How many lines of symmetry in an equilateral triangle?
3
If the preimage is B(-1, -2), and the vector used for translation is <3,2> what is the image?
B' (2, 0)
The coordinates of the preimage are A(-1, 4), B(3, 4), C(2, -1), D(0, 1). After a counterclockwise 270 degree rotation, what are the coordinates of the image?
A'(4, 1)
B'(4, -3)
C'(-1, -2)
D'(1 ,0)
Frankie reflects the point P(−2, 6) across the line y = −x and then across the y-axis. What are the coordinates of the point after the reflections?
P"(6, 2)
How many lines of symmetry in a rectangle?
2
Randy leaves his house and walks 5 blocks north and then 2 blocks east to get to the library. Write a single translation vector that describes the change from his house to the library. If Randy’s house is located at the point (6, −3) on a map, and each unit represents 1 block, what is the location of the library on the map?
<2, 5>
(8, 2)
Hong is playing a board game and spins a spinner. Before spinning, the point of the spinner is at (-2, 6). After spinning, the point is at (-6, -2). What is the angle of rotation between the starting point and ending point of the spinner?
90 degree counterclockwise rotation
Michael says that reflecting a point across the x-axis and then reflecting the point again across the y-axis is the same as rotating the point 180° counterclockwise. Is he correct?
Yes
How many lines of symmetry does a circle have?
Infinitely many
Given the coordinates A(1,3), B(1, 1), and C(4, 4)
1) Translate using the vector <-1, -2>
2) Rotate your new coorindates 90 degrees counterclockwise
3) Reflect your new figure over the line y=x
What are the final coordinates?
A'''(0, -1)
B''' (0, 1)
C'''(3, -2)
Students are asked to find the coordinates of the image of F (5, −2), G (3, 4), and H(−2, 3) after it is translated using the vector 〈−3, 3〉. Ross says the coordinates are F′(8, −5), G′(6, 1), and H′(1, 0). Samantha says the coordinates are F′(2, 1), G′(0, 7), and H′(−5, 6). Who is correct?
Samantha
Cindy says that she has a regular polygon in her hands that rotates onto itself when rotated 90° (this is the smallest angle of rotation). What regular polygon does Cindy have?
Square
Marco reflects the triangle X(4, −5), Y(4, -2), Z (5, −4) across the line x = 3, and then reflects the image across the y-axis. What are the coordinates of the triangle after being reflected across the y-axis?
X(4, -5) → X′(2, −5) → X″(−2, −5)
Y(4, -2) → Y′(2, −2) → Y″(−2, −2)
Z(5, -4) → Z′(1, −4) → Z″(−1, −4)
Reggie states that a counterclockwise rotation of 216° will map a regular pentagon onto itself. Is Reggie correct?
Yes
Given the points A(4, -2), B(1, -1), C(-3, 2) and the vector 〈−2, 5〉, what are the coordinates of the image?
A'(2, 3)
B'(-1, 4)
C'(-5. 7)
Given the preimage of a triangle with vertices at L(4, -6), M(5, -1), and N(7, -3), rotate the image counterclockwise 810°. What are the coordinates of the vertices of the image?
L'(6, 4)
M'(1, 5)
N'(3, 7)
A triangle with the vertices A(-4, -3), B(-1, -3), and C(-5, -5) is reflected across the line y = -2 and then across the y-axis. What are the ending coordinates?
A"(4, -1)
B"(1, -1)
C"(5, 1)
Alexandra and Maris are playing a game where they guess how many sides the regular polygon the other is holding has. Alexandra says her regular polygon has exactly 12 lines of symmetry. Maris says her regular polygon has an angle of rotational symmetry of 24°. How many sides does each regular polygon have?
Alexandra: 12 sided polygon
Maris: 15 sided polygon