Transformation Rules Flashcards

Questions and Answers

What is the transformation that turns a figure about a fixed point through a given angle and direction?

Translation

Dilation

Reflection

Rotation (correct)

What happens to the coordinates (x,y) during a 90 degrees CCW rotation about the origin?

(-y,x)

How do the coordinates (x,y) change during a 270 degrees CCW rotation about the origin?

(y,-x)

What is the result of a 180 degrees rotation about the origin on the coordinates (x,y)?

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

What is the transformation for a translation given the rule (x,y) goes to (x+a,y+b)?

Translation Signup and view all the answers

What effect does reflection over the x-axis have on the coordinates (x,y)?

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

How do the coordinates (x,y) change during reflection over the y-axis?

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

What happens to (x,y) when reflected over the line y = x?

(y,x) Signup and view all the answers

What is the result of reflecting (x,y) over the line y = -x?

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

What happens to the coordinates (x,y) during dilation by a scale factor of a?

(ax,ay) Signup and view all the answers

What is the effect when a > 1 during dilation?

Enlarged Signup and view all the answers

What happens when a < 1 during dilation?

Reduced Signup and view all the answers

What is the definition of a transformation?

The mapping of all points of a figure according to a common operation. Signup and view all the answers

What does reflection mean in geometric terms?

A transformation that flips a figure over a line. Signup and view all the answers

What is an isometry?

A transformation that preserves size and shape. Signup and view all the answers

What is the scale factor in similar figures?

The ratio of corresponding lengths of two similar figures. Signup and view all the answers

What are congruent figures?

Figures that have the same size and shape. Signup and view all the answers

What are similar figures?

Figures that have the same shape but not necessarily the same size. Signup and view all the answers

Study Notes

Transformation Rules

Rotation 90 degrees CCW about the origin: Transforms point (x,y) to (-y,x).
Rotation 180 degrees about the origin: Transforms point (x,y) to (-x,-y).
Rotation 270 degrees CCW about the origin: Transforms point (x,y) to (y,-x).
Rotation 90 degrees CW about the origin: Transforms point (x,y) to (y,-x) (same result as 270 degrees CCW).

Translation and Reflection

Translation: Moves point (x,y) to (x+a,y+b), denoting a shift along the axes based on values a and b.
Reflection over the x-axis: Transforms point (x,y) to (x,-y), flipping it vertically.
Reflection over the y-axis: Transforms point (x,y) to (-x,y), flipping it horizontally.
Reflection over y = x: Transforms point (x,y) to (y,x), swapping coordinates.
Reflection over y = -x: Transforms point (x,y) to (-y,-x), flipping coordinates diagonally.

Dilation and Image Properties

Dilation by scale factor a: Transforms point (x,y) to (ax,ay), modifying distances from the center by the scale factor.
If a > 1: The figure enlarges, increasing in size.
If a < 1: The figure reduces in size.

Basics of Transformations

Transformation: General mapping of all points of a figure in a plane based on a common operation.
Reflection: A flip over a particular line to create a mirror image.
Rotation: Turning a figure about a fixed point through a specified angle and direction.
Angle of Rotation: The degree of rotation around a fixed point.

Congruence and Similarity

Congruent Figures: Identical in size and shape, map directly onto each other.
Similar Figures: Identical shape but different sizes; corresponding angles are congruent, and sides are proportional.
Scale Factor: The proportional relationship between corresponding lengths of two similar figures.
Corresponding Lengths: Sides in similar figures that maintain the same relative positions.
Corresponding Angles: Angles sharing the same relative position in geometric figures.

Preimage and Isometry

Preimage: The original figure before any transformation occurs.
Isometry: A transformation preserving both size and shape, resulting in congruent figures; often referred to as rigid transformations.

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Description

Test your knowledge on transformation rules with these flashcards. This quiz covers various types of rotations and translations, providing definitions for each transformation. Perfect for students needing practice with geometric transformations.