24 Questions
What is the definition of translation in transformation geometry?
Moves every point of a shape the same distance in the same direction
What is the notation for translation in transformation geometry?
(x, y) → (x + a, y + b)
What is the center of rotation in rotation transformation?
A fixed point that does not change
What is the formula for a 90° counterclockwise rotation about the origin?
(x, y) → (-y, x)
What is the formula for reflection over the x-axis?
(x, y) → (x, -y)
What is the definition of dilation in transformation geometry?
Changes the size of a shape but not its shape
What is the formula for dilation from the origin with a scale factor of k?
(x, y) → (kx, ky)
What is the key element that determines how much the shape is enlarged or reduced in dilation?
Scale factor
What is the effect of a translation on a shape?
It moves every point of the shape the same distance in the same direction.
What is the horizontal shift in the notation (x, y) → (x + a, y + b)?
a
What is the result of a 180° rotation about the origin?
(x, y) → (-x, -y)
What is the line of reflection in the formula (x, y) → (y, x)?
y = x
What is the effect of a dilation with a scale factor of 2 on a shape?
It enlarges the shape to twice its size.
What is the center of dilation in the formula (x, y) → (kx, ky)?
The origin
What type of transformation is represented by the formula (x, y) → (x - 3, y + 2)?
Translation
What is the direction of rotation in a 270° counterclockwise rotation about the origin?
Counterclockwise
What is the result of a translation by vector (3, 4) and then a reflection over the x-axis?
(x + 3, y - 4)
What is the effect of a rotation of 90° counterclockwise about the origin followed by a dilation with a scale factor of 2?
(-2y, 2x)
What is the result of a reflection over the line y = x followed by a reflection over the y-axis?
(-x, y)
What is the result of a translation by vector (-2, 3) followed by a 180° rotation about the origin?
(x - 4, y + 6)
What is the effect of a dilation with a scale factor of 3 followed by a reflection over the x-axis?
(3x, -3y)
What is the result of a 270° counterclockwise rotation about the origin followed by a translation by vector (4, -2)?
(x - 4, y + 2)
What is the effect of a reflection over the y-axis followed by a dilation with a scale factor of 2?
(-2x, 2y)
What is the result of a translation by vector (1, 2) followed by a 90° counterclockwise rotation about the origin?
(x - 2, y + 1)
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