Gr 9 MATH: Ch 10.1 Transformations

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What is the definition of translation in transformation geometry?

Changes the size of a shape but not its shape

Moves every point of a shape the same distance in the same direction (correct)

Rotates a shape around a fixed point

Flips a shape over a line called the line of reflection

What is the notation for translation in transformation geometry?

(x + a, y + b) → (x, y)

(x + a, y) → (x, y + b)

(x, y + b) → (x + a, y)

(x, y) → (x + a, y + b) (correct)

What is the center of rotation in rotation transformation?

A point that rotates with the shape

A point that moves in the same direction as the shape

A fixed point that does not change (correct)

The origin of the coordinate plane

What is the formula for a 90° counterclockwise rotation about the origin?

(x, y) → (-y, x) Signup and view all the answers

What is the formula for reflection over the x-axis?

(x, y) → (x, -y) Signup and view all the answers

What is the definition of dilation in transformation geometry?

Changes the size of a shape but not its shape Signup and view all the answers

What is the formula for dilation from the origin with a scale factor of k?

(x, y) → (kx, ky) Signup and view all the answers

What is the key element that determines how much the shape is enlarged or reduced in dilation?

Scale factor Signup and view all the answers

What is the effect of a translation on a shape?

It moves every point of the shape the same distance in the same direction. Signup and view all the answers

What is the horizontal shift in the notation (x, y) → (x + a, y + b)?

a Signup and view all the answers

What is the result of a 180° rotation about the origin?

(x, y) → (-x, -y) Signup and view all the answers

What is the line of reflection in the formula (x, y) → (y, x)?

y = x Signup and view all the answers

What is the effect of a dilation with a scale factor of 2 on a shape?

It enlarges the shape to twice its size. Signup and view all the answers

What is the center of dilation in the formula (x, y) → (kx, ky)?

The origin Signup and view all the answers

What type of transformation is represented by the formula (x, y) → (x - 3, y + 2)?

Translation Signup and view all the answers

What is the direction of rotation in a 270° counterclockwise rotation about the origin?

Counterclockwise Signup and view all the answers

What is the result of a translation by vector (3, 4) and then a reflection over the x-axis?

(x + 3, y - 4) Signup and view all the answers

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) Signup and view all the answers

What is the result of a reflection over the line y = x followed by a reflection over the y-axis?

(-x, y) Signup and view all the answers

What is the result of a translation by vector (-2, 3) followed by a 180° rotation about the origin?

(x - 4, y + 6) Signup and view all the answers

What is the effect of a dilation with a scale factor of 3 followed by a reflection over the x-axis?

(3x, -3y) Signup and view all the answers

What is the result of a 270° counterclockwise rotation about the origin followed by a translation by vector (4, -2)?

(x - 4, y + 2) Signup and view all the answers

What is the effect of a reflection over the y-axis followed by a dilation with a scale factor of 2?

(-2x, 2y) Signup and view all the answers

What is the result of a translation by vector (1, 2) followed by a 90° counterclockwise rotation about the origin?

(x - 2, y + 1) Signup and view all the answers