Nature of Mathematics: Transformations

What occurs when a figure moves from one place to another on a coordinate plane?

It is common practice to name original shapes using _____ letters.

Transformed shapes are named using the same letters but with a ______ symbol.

Which of the following is NOT one of the four basic types of transformations?

What is translation in terms of transformation?

What does reflection do to a figure?

What is a rotation in geometric transformations?

Which of the following is an example of a tessellation?

Nature of Mathematics

Movement of figures on a coordinate plane results in a transformation, changing the figure's position.
Original shapes are labeled with capital letters; transformed shapes use the same letters with a "prime symbol."

Patterns and Numbers in Nature

Patterns in nature reflect visible regularities and are crucial for understanding natural processes.
Mathematical patterns can include numerical, visual, logic, and word patterns, with number patterns being most common.

Transformation Types

Translation (Slide):
- Moves each point of a figure the same distance and direction.
- Size, shape, and direction remain unchanged.
- Example: Movement of jumping animals like kangaroos and frogs.
Reflection (Flip):
- Flips a figure over a line (line of reflection).
- The original figure and its reflection have identical shapes and sizes but face opposite directions.
- Example: Light reflection.
Rotation (Turn):
- Rotates a figure around a fixed point, termed the center of rotation.
- The shape and size of the figure stay constant, but orientation changes based on the angle of rotation.

Tessellation

Defined as a repeating pattern made with regular polygons with no gaps or overlaps.
Each vertex in a tessellated shape remains consistent, creating a visual illusion.
Examples of tessellations in nature include beehives, pineapples, and turtle shells.
M.C. Escher is notable for his use of tessellations in art.

Explore the fascinating world of mathematical transformations, including translation, reflection, and rotation on a coordinate plane. This quiz will help you understand how figures change position while maintaining their properties. Delve into the patterns in nature that highlight the importance of mathematics in understanding our surroundings.