Pre-Algebra Transformations Flashcards

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Questions and Answers

What is a transformation?

To manipulate the shape of an object

What is a translation?

A transformation that slides an object

What is a reflection?

A transformation that flips an object over a line or point

What is rotation?

A transformation that turns an object Signup and view all the answers

What is a vector?

A directed segment that has direction and magnitude (length) Signup and view all the answers

What is rigid motion?

A transformation that preserves distance and angle measure Signup and view all the answers

What does congruent mean?

2 figures that have the same size and shape Signup and view all the answers

What is vector translation?

Use the length and dimension of the vector to translate the pre-image Signup and view all the answers

What is description translation?

Use the units and direction in the description to translate the pre-image Signup and view all the answers

What is mapping translation?

For x: subtraction moves left, addition moves right; For y: subtraction moves down, addition moves up Signup and view all the answers

What is notation translation?

For x: negative moves left, positive moves right; For y: negative moves down, positive moves up Signup and view all the answers

What is r x-axis?

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

What is r y-axis?

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

What does r y=#/r x=# refer to?

Count number of units from pre-image to the line of reflection, plot image the same number of units away from line of reflection on the opposite side Signup and view all the answers

What is r y=x?

(y,x) Signup and view all the answers

What is r y=-x?

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

What is R 90?

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

What is R -90?

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

What is R 180/R -180?

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

How do you rotate an object around a point other than the origin?

Create a new set of axes and then use the rules listed above Signup and view all the answers

Study Notes

Transformations Overview

Transformation refers to the manipulation of an object's shape or position in space.
Essential for understanding geometry and spatial relationships.

Types of Transformations

Translation: Slides an object without changing its shape or size; maintains orientation.
Reflection: Flips an object over a specific line or point, essentially creating a mirror image.
Rotation: Turns an object around a fixed point, changing its orientation while keeping the shape unchanged.

Vector and Motion

Vector: A segment that has both direction and magnitude (length), essential in defining translations.
Rigid Motion: A transformation that keeps the distances and angles unchanged between points, ensuring the figures remain congruent.

Congruence

Congruent Figures: Two figures that have the same shape and size, crucial for understanding similarities in geometry.

Translation Techniques

Vector Translation: Utilizes the vector's length and direction to determine how to move the pre-image.
Description Translation: Involves translating based on explicit descriptions of units and directions.
Mapping Translation: In this method, subtracting moves the object left (for x) or down (for y), while adding moves it right (for x) or up (for y).
Notation Translation: For x-axis movements, negative indicates left, and positive indicates right; for y-axis, negative moves down and positive moves up.

Reflection Rules

Reflection over x-axis: Changes the coordinates to (x, -y).
Reflection over y-axis: Changes the coordinates to (-x, y).
Reflection over a specific line (y = # or x = #): Measure the distance from the pre-image to the line and plot the image the same distance on the opposite side.

Special Reflections and Rotations

Reflection over y = x: Switches coordinates to (y, x).
Reflection over y = -x: Coordinates change to (-y, -x).
Rotation of 90°: Results in coordinates changing to (-y, x).
Rotation of -90°: Results in coordinates changing to (y, -x).
Rotation of 180° (or -180°): Both coordinates become negative, resulting in (-x, -y).

Rotation Around Other Points

To rotate an object at angles other than 90°, create new axes and apply the established rotation rules based on the new coordinates.

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Description

Dive into the essential concepts of transformations in pre-algebra with these flashcards. Each card presents a key term related to transformations such as translation, reflection, rotation, and vectors, complete with clear definitions. This set serves as an excellent study tool for mastering geometric manipulations.