Geometric Transformations Practice Flashcards

Vocabulary terms, definitions, and mathematical formulas for geometric transformations based on the lecture notes.

Geometric transformations

The changes made to the position, size, or shape of geometric figures including triangles, squares, circles, or any other shape.

Pre-image

The figure we start with before any transformation is made.

Image

The resulting figure after completing a geometric transformation.

Rigid transformations

Transformations including translation, reflection, and rotation that keep the shape and size of the figure the same before and after the change.

Non-rigid transformation

A transformation, such as dilation, that changes the size of the figure while preserving its shape.

Translation

A type of geometric transformation where a figure is moved or slid from one place to another in a straight line (horizontally, vertically, or diagonally) without rotating or changing its size.

Reflection

A geometric transformation where a figure is flipped across a line called the "line of reflection" to create a mirror image.

Line of reflection

The line across which a figure is flipped during a reflection.

Rotation

A geometric transformation where a figure is turned around a fixed point called the "center of rotation" by a certain amount measured in degrees.

Center of rotation

The fixed point around which a figure is turned during a rotation.

Dilation

A geometric transformation where the size of a figure is changed (enlarged or shrunk) while its shape is kept the same.

Center of dilation

The fixed center point towards or away from which each point of a figure moves during a dilation.

Scale factor

A factor that determines how much larger or smaller a figure becomes during a dilation.

Conservation of Properties

The principle that geometric properties like side lengths, angle measurements, and area do not change with translations, reflections, and rotations.

Mathematical Representation

Formulas or coordinates on the coordinate plane that map each point of the pre-image to its corresponding point in the transformed image.

Horizontal Translation Formula

$$(x, y) \rightarrow (x + k, y)$$

Vertical Translation Formula

$$(x, y) \rightarrow (x, y + j)$$

Reflection over x-axis Formula

$$(x, y) \rightarrow (x, y)$$

Reflection over y-axis Formula

$$(x, y) \rightarrow (-x, y)$$

Rotation $90^\circ$ clockwise about the origin Formula

$$(x, y) \rightarrow (y, -x)$$

Rotation $90^\circ$ counterclockwise Formula

$$(x, y) \rightarrow (-y, x)$$

Rotation $180^\circ$ about the origin clockwise and counterclockwise Formula

$$(x, y) \rightarrow (-x, -y)$$

Rotation $270^\circ$ clockwise Formula

$$(x, y) \rightarrow (-y, x)$$

Rotation $270^\circ$ counterclockwise Formula

$$(x, y) \rightarrow (y, -x)$$

Rotation $360^\circ$ clockwise or counterclockwise Formula

$$(x, y) \rightarrow (x, y)$$

Dilation from the origin Formula

$$(x, y) \rightarrow (kx, ky)$$

Example of Real-life Translation

Pushing a toy car along a straight path is a great example of transla5on.