Vocabulary
A flip that creates a mirror image of a figure across a line.
Reflection
Identify the reflection: (−3,7)→(3,7)
Reflection across the y-axis
True or False: A translation changes the size and shape of a figure.
False
What is the image of (3,2) after a 90° clockwise rotation about the origin?
(2,−3)
True or False: Every figure with rotational symmetry has point symmetry.
False
A slide that moves a figure left, right, up, or down without turning or changing its size.
Translation
What happens to the coordinates of a point when it is reflected over the x-axis?
(x,y)→(x,−y)
What is the translation rule that moves a point 3 units left and 5 units down?
(x,y)→(x−3,y−5)
What is the image of (−4,1) after a 180° rotation about the origin?
(4,−1)
A figure has two matching halves when folded along a line. What type of symmetry does it have?
Reflection (Line) Symmetry
A turn or spin of a figure around a fixed point.
Rotation
What is the image of (3,5) after a reflection over the x-axis?
(3,−5)
Identify the translation: (2,−1)→(−4,6).
6 left and 7 up
A point is rotated 90° counterclockwise about the origin. What happens to its coordinates?
(x,y)→(−y,x)
A figure looks the same after being rotated 180° around its center. What type of symmetry does it have?
Point Symmetry
A move (like translation, reflection, or rotation) that keeps the exact same size and shape.
Rigid Transformation
Point A(2,−6) is reflected over the line y=x. What are the coordinates of A′?
(−6,2)
A point (2,3) is translated 4 units right and 2 units up. What are the coordinates of its image?
(6,5)
A triangle is transformed from A(1,2) to A′(−2,1). What rotation occurred?
90° counterclockwise
A regular hexagon has how many lines of symmetry?
6
The resulting new figure after a transformation is applied, often labeled with prime notation (A').
Image
A point (4,−7) is reflected across the y-axis and then across the x-axis. What are the final coordinates?
(−4,7)
A point (x,y) is translated 5 units left and 8 units up to become (−2,11). What were the original coordinates?
(3,3)
A point (x,y) is rotated 90° clockwise about the origin and becomes (−6,4). What were the original coordinates?
(4,6)
What is the smallest angle of rotation that maps a regular pentagon onto itself?
72°