Geometry: Unit 3 (Transformations)

Flashcards covering core vocabulary, definitions, and properties of geometric transformations including translations, reflections, rotations, and dilations.

Transformation

A change of a figure into another figure, categorized into four types: reflection, translation, dilation, and rotation.

Pre-image

The old or original figure prior to a transformation.

Image

The new figure resulting from a transformation.

Prime

The notation used to label an image resulting from a transformation, such as $A'$ for 'A prime'.

The Distance Formula

$\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$, used to find the distance between two points given on a graph or as two written ordered pairs.

Translation

A transformation also known as a slide or shift; it is isometric, preserves orientation, and can be achieved by performing two composite reflections over parallel lines.

Translation Coordinate Rule

$(x, y) \rightarrow (x+h, y+k)$, where $h$ is the horizontal shift (negative if moving left) and $k$ is the vertical shift (negative if moving down).

Reflection

A transformation that is a flip performed over a line of reflection; it is isometric but does not preserve orientation.

Line of Reflection

The line over which a figure is flipped in a reflection; lines of symmetry are examples of lines of reflection.

Line Symmetry

A characteristic of a figure when a line divides it into congruent parts, acting as a fold line where the image stacks perfectly on top of itself.

Dilation

A transformation that changes the size of a figure without changing its shape, enlarging or reducing it with respect to a point called the center of dilation.

Center of Dilation

The reference point (point of projection) with respect to which a figure is enlarged or reduced.

Enlargement

A dilation where the resulting after-image is bigger than the original image.

Shrink

A dilation where the resulting after-image is smaller than the original image.

Rotation

A transformation that is a turn; it is isometric, does not preserve orientation unless rotated $360^\circ$ or onto itself, and can be achieved by two composite reflections over intersecting lines.

180° Rotation Rule

$(x, y) \rightarrow (-x, -y)$, which is equivalent to a reflection through the origin.