Finite Mathematics 1: Geometric Translations Flashcards

This set covers vocabulary and core concepts regarding geometric translations, including methods of notation, vector components, and related theorems from the Week 2 lecture.

Translation

A movement where a figure moves or slides to a new position while keeping the same size, shape, and orientation.

Preimage

The original figure before a geometric transformation is applied.

Image

The new figure formed after a transformation, often denoted with prime notation such as $P'$.

Congruent

A property where a translation retains the shape of the original figure such that the image is identical in size and shape to the preimage.

Verbal Description Method

A method that uses words to describe the movement of a shape, such as "Translate the figure 3 units to the right & 6 units downwards."

Coordinate Mapping Method

A description of translations in a coordinate plane using the notation $(x, y) \rightarrow (x + a, y + b)$ where $a$ and $b$ are constants.

Vector

A quantity that has both direction and magnitude (or size) and is represented by an arrow drawn between two points.

Initial Point

The starting point of a vector.

Terminal Point

The ending or final point of a vector.

Component Form

The notation of a vector that combines its horizontal and vertical components, written as $\langle 5, 3 \rangle$ for a horizontal shift of 5 and vertical shift of 3.

Symbol or Notation Method

A method using the symbol $T_{x,y}$ where $T$ stands for "Translation" and the listed $(x, y)$ values indicate the movement of every vertex.

Theorem 7.4 (Translation Theorem)

Statment that a translation is an isometry.

Isometry

A transformation that preserves length and distance, as seen in geometric translations.

Theorem 7.5 (Reflections in Parallel Lines)

If lines $k$ and $m$ are parallel, then a reflection in line $k$ followed by a reflection in line $m$ is a translation.

Magnitude

The size or length associated with a vector.

Horizontal Component

The value in a vector's component form representing the distance and direction a point moves along the x-axis.

Vertical Component

The value in a vector's component form representing the distance and direction a point moves along the y-axis.