Transformations and Symmetry

Front

What is a transformation in geometry?

Back

A transformation is an operation that moves or changes a shape in some way to produce a new shape. Common types include translations, rotations, reflections, and dilations.

Front

Define translation in geometry.

Back

Translation is a type of transformation that slides a shape from one position to another without turning it. It is defined by a vector that indicates the direction and distance of the slide.

Front

What is the rule for translating a point (x, y) by (a, b)?

Back

The rule for translating a point (x, y) by (a, b) is (x, y) --> (x + a, y + b).

Front

What does it mean to dilate a shape?

Back

Dilation is a transformation that changes the size of a shape but not its shape. It is defined by a scale factor.

Front

What is the scale factor in dilation?

Back

The scale factor is a number that scales, or multiplies, the dimensions of a shape. A scale factor greater than 1 enlarges the shape, while a scale factor between 0 and 1 reduces it.

Front

How do you determine if two triangles are similar?

Back

Two triangles are similar if their corresponding angles are equal and the lengths of their corresponding sides are proportional.

Front

What is the relationship between rotation and the center of rotation?

Back

Rotation is a transformation that turns a shape around a fixed point called the center of rotation. The angle of rotation determines how far the shape is turned.

Front

Define reflection in geometry.

Back

Reflection is a transformation that flips a shape over a line, creating a mirror image. The line is called the line of reflection.

Front

What is symmetry in geometry?

Back

Symmetry in geometry refers to a balance or similarity between two halves of a shape. A shape is symmetric if it can be divided into two identical parts.

Front

What is the difference between rigid and non-rigid transformations?

Back

Rigid transformations preserve the shape and size of a figure (e.g., translations, rotations, reflections), while non-rigid transformations change the size or shape (e.g., dilations).