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Algebraic Representations Quiz

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Questions and Answers

What is the algebraic representation of translation?

(x,y)~(x+a, y+b) (correct)

(x,y)~(y, -x)

(x,y)~(-x, y)

(x,y)~(-y,x)

What is the algebraic representation of reflection over the x-axis?

(x,y)~(x, -y) (correct)

(x,y)~(-x, y)

(x,y)~(x+a, y+b)

(x,y)~(-y, x)

What is the algebraic representation of reflection over the y-axis?

(x,y)~(-y, x)

(x,y)~(x+a, y+b)

(x,y)~(-x, y) (correct)

(x,y)~(y, -x)

What is the algebraic representation of a 90 degree clockwise rotation about the origin?

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

What is the algebraic representation of a 180 degree clockwise rotation about the origin?

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

What is the algebraic representation of a 270 degree clockwise rotation about the origin?

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

Study Notes

Algebraic Representations of Transformations

Translation: Represents movement of a point without rotation. The point (x,y) translates to (x+a, y+b).
Reflection over the x-axis: Reflects points by inverting the y-coordinate. The transformation changes (x,y) to (x,-y).
Reflection over the y-axis: Inverts the x-coordinate for reflection across the y-axis. The transformation converts (x,y) to (-x,y).
90 Degree Clockwise Rotation: Points are rotated 90 degrees clockwise around the origin, transforming (x,y) to (y,-x).
180 Degree Clockwise Rotation: A point rotates halfway around the origin; (x,y) is transformed to (-x,-y).
270 Degree Clockwise Rotation: This rotation results in a transformation from (x,y) to (-y,x), effectively turning points around the origin three-quarters of the way.

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Description

Test your knowledge on algebraic representations related to transformations in geometry. This quiz covers translations, reflections, and rotations in a coordinate plane. Perfect for students looking to strengthen their understanding of algebraic concepts.