Geometry Transformations Flashcards

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Questions and Answers

What is a dilation?

A transformation that enlarges or reduces a figure (correct)

A transformation that flips a figure over a line

A transformation that turns a figure around a point

A transformation that slides points

What is the center of dilation?

The point of intersection of lines through each pair of corresponding vertices in a dilation.

Define the scale factor.

The ratio used to enlarge or reduce similar figures.

What does 'congruent' mean?

Having the same size and shape Signup and view all the answers

What is a translation?

A transformation that slides each point of a figure the same distance in the same direction. Signup and view all the answers

What does reflection mean in geometry?

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

What is rotation in geometry?

A transformation in which a figure is turned around a point. Signup and view all the answers

What is a transformation?

A movement of a geometric figure. Signup and view all the answers

A 360° rotation changes the coordinates of a point.

False Signup and view all the answers

What is a 90° rotation clockwise transformation?

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

What is the reflection across the x-axis transformation?

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

What is the reflection across the y-axis transformation?

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

What does similarity mean in geometry?

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

What does a dilation enlargement with a scale factor greater than 1 indicate?

It enlarges the figure. Signup and view all the answers

What does a dilation reduction with a scale factor less than 1 indicate?

It reduces the figure. Signup and view all the answers

What is the pre-image in a transformation?

The original image of a figure in a transformation. Signup and view all the answers

What is the image in a transformation?

The resulting point or set of points under a transformation. Signup and view all the answers

Study Notes

Dilation and Transformations

Dilation is a transformation that alters the size of a figure, either enlarging or reducing it.
Enlargement increases all dimensions proportionately, while reduction decreases all dimensions in the same ratio.
The center of dilation is the intersection point from lines drawn between corresponding vertices of the original and transformed figures.
Scale factor indicates the ratio used for enlarging or reducing figures.

Geometric Transformations

Congruent figures have identical size and shape, crucial for understanding transformations.
Translation refers to the sliding of a figure in a specified direction by a uniform distance.
Reflection is when a figure is flipped over a predefined line, also known as a mirror line.
Rotation involves turning a figure around a specific point by a set angle (e.g., 90°, 180°, 270°, 360°).

Properties of Transformations

A 360° rotation results in coordinates that remain unchanged.
Scaling describes the ratio between two measurement sets, important for understanding size changes.
Different types of reflections alter coordinates:
- Reflection across the x-axis transforms (x,y) to (x,-y).
- Reflection across the y-axis changes (x,y) to (-x,y).
- Reflection across the origin results in (x,y) becoming (-x,-y).

Dilation Types

Dilation enlargement can be represented as (x,y) transforming to (2x, 2y) or (4x, 4y) with a scale factor greater than 1.
Dilation reduction transforms coordinates like (x,y) to (.5x, .5y) or (1/2x, 1/2y) with a scale factor less than 1.

Similarity and Transformation Concepts

Similar shapes share the same form but differ in dimension.
An image is the resultant set of points after applying a transformation, denoted as (p', r', x').
The pre-image is the figure prior to transformation, marked as (p, r, x).
Transformation specific effects on rotation include:
- 90-degree clockwise: (x,y) → (y,-x)
- 90-degree counterclockwise: (x,y) → (-y,x)
- 180-degree: (x,y) → (-x,-y)
- 270-degree clockwise: (x,y) → (-y,x)

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Description

Explore key concepts in geometry with our flashcards on dilation, enlargement, reduction, and the center of dilation. Perfect for students looking to understand these transformations better. Test your knowledge and reinforce your learning!