Transformations Vocabulary
What is the term for a transformation that "slides" a figure to a new position without changing its shape or size?
Translations
What happens to a point (x, y) if it is translated 3 units to the right?
(x,y) ---> (x+3,y)
Reflect the point (3, -4) across the x-axis. What is the new point?
(3, 4)
Rotate the point (2, 3) 90° counterclockwise around the origin. What is the new point?
(-3, 2)
A figure is translated 3 units to the left and then 2 units up. What is the rule for this transformation?
(x, y) → (x - 3, y + 2)
What is the name of the transformation that "flips" a figure over a line?
Reflections
Translate the point (4, -2) 5 units down and 4 units right. What is the new point?
(8,-7)
What is the rule for reflecting a point across the y-axis?
(x, y) → (-x, y)
What is the rule for a 180° rotation around the origin?
(x, y) → (-x, -y)
Rotate the point (-3, 2) 180° around the origin. What is the final point?
(3, -2)
What do we call a transformation that "turns" a figure around a fixed point?
Rotations
A triangle is translated according to the rule (x, y) → (x - 2, y + 4). What happens to the triangle?
It moves 2 units left and 4 units up
What line of reflection would map the point (4, 7) onto (-4, 7)?
The y-axis
Rotate the point (-5, 1) 90° clockwise around the origin. What is the new point?
(1, 5)
Reflect the point (2, -3) across the x-axis. What is the final point?
(2,3)
What is the term for the line or axis that a figure is reflected over?
Line of reflection
What is the translation rule if point A(2, 5) moves to A'(7, 8)?
(x, y) → (x + 5, y + 3)
A triangle has vertices at (1, 2), (3, 4), and (5, 6). Reflect it across the y-axis. What are the new vertices?
(-1, 2), (-3, 4), (-5, 6)
A rectangle is rotated 270° counterclockwise. Is this the same as a 90° clockwise rotation?
Yes
A point (3, 4) is translated 2 units down. What is the new point?
(3,2)
What is the fixed point called in a rotation?
Center of Rotation
A square with vertices at (0, 0), (2, 0), (2, 2), and (0, 2) is translated by (x, y) → (x - 4, y + 1). What are the new coordinates of the vertices?
(-4, 1), (-2, 1), (-2, 3), (-4, 3)
Reflect the point (-2, 5) across the x-axis
(-2,-5)
If a figure is rotated 360°, how does it compare to its original position?
It is unchanged.
A figure is translated 3 units to the left and then 2 units up. What is the rule for this transformation?
(x, y) → (x - 3, y + 2)