Transformations and Dilations Algebraic Rules

Questions and Answers

What is the algebraic rule for reflection across the y-axis?

(x,y)→(-x, y) (correct)

(x,y)→(x,-y)

(x,y)→(-x,-y)

(x,y)→(3x,3y)

What is the algebraic rule for reflection across the x-axis?

(x,y)→(x,-y) (correct)

(x,y)→(3x,3y)

(x,y)→(-x,-y)

(x,y)→(-x, y)

What is the algebraic rule for a dilation with a scale factor of three?

(x,y)→(1/2x, 1/2y)

(x,y)→(3x,3y) (correct)

(x,y)→(2x, 2y)

(x,y)→(x,y)

What is the algebraic rule for a dilation with a scale factor of one-half?

(x,y)→(1/2x, 1/2y) Signup and view all the answers

What is the algebraic rule for a rotation of 90° clockwise?

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

What is the algebraic rule for a rotation of 90° counterclockwise?

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

What does the transformation (x,y)→(x + 5, y - 3) represent?

Translate right 5 and down 3 Signup and view all the answers

What does the transformation (x,y)→(2x, 2y) represent?

Dilation with a scale factor of 2 Signup and view all the answers

What does the transformation (x,y)→(-x, y) represent?

Reflection across the y-axis Signup and view all the answers

What does the transformation (x,y)→(-x,-y) represent?

180° Rotation Signup and view all the answers

What does the transformation (x, y)→(x-4, y + 7) represent?

Translating left 4 and up 7 Signup and view all the answers

What does the transformation (x, y)→(4x, 4y) represent?

Dilation with a scale factor of 4 Signup and view all the answers

Study Notes

Transformations and Dilations Algebraic Rules

Reflection across the y-axis alters coordinates from (x,y) to (-x,y), changing the sign of the x-coordinate.
Reflection across the x-axis changes coordinates from (x,y) to (x,-y), altering the sign of the y-coordinate.
Dilation with a scale factor of three transforms coordinates to (3x,3y), enlarging the figure by three times.
A dilation with a scale factor of one-half alters coordinates to (1/2x, 1/2y), reducing the figure to half its size.
A rotation of 90° clockwise changes coordinates from (x,y) to (y,-x), shifting positions in a circular manner.
A rotation of 90° counterclockwise alters coordinates from (x,y) to (-y,x), also rotating points circularly but in the opposite direction.
The translation rule (x,y)→(x + 5, y - 3) moves points 5 units to the right and 3 units down on a Cartesian plane.
The dilation rule (x,y)→(2x, 2y) expands figures by a scale factor of 2, doubling the size of the original figure.
The transformation (x,y)→(-x,y) indicates reflection across the y-axis, which flips the figure horizontally.
The transformation (x,y)→(-x,-y) represents a 180° rotation, flipping the figure across both axes.
Translating points left 4 and up 7 is described by (x, y)→(x-4, y + 7), moving the position of points effectively in two directions.
A dilation represented by (x,y)→(4x, 4y) increases the size of the figure by a scale factor of 4, quadrupling its dimensions.

Description

Test your knowledge of algebraic rules for transformations and dilations. This quiz covers reflections across the x and y axes as well as dilations with different scale factors. Perfect for strengthening your understanding of geometric transformations in algebra.