Transformations & Symmetry Flashcard Review

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 transformations include translations, rotations, reflections, and dilations.

Front

Define rotation in the context of transformations.

Back

Rotation is a transformation that turns a shape around a fixed point, known as the center of rotation, by a certain angle in a specified direction.

Front

What is a line of symmetry?

Back

A line of symmetry is a line that divides a shape into two identical parts that are mirror images of each other.

Front

How do you determine the number of lines of symmetry in a shape?

Back

To determine the number of lines of symmetry, you can fold the shape along potential lines and check if both halves match perfectly.

Front

What is a translation in geometry?

Back

A translation is a transformation that slides a shape from one position to another without rotating or flipping it. It is defined by a vector that indicates the direction and distance of the slide.

Front

Explain reflection in geometric transformations.

Back

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

Front

What is the effect of a 90° clockwise rotation on a point (x, y)?

Back

The new coordinates after a 90° clockwise rotation about the origin are (y, -x).

Front

What is the effect of a 180° rotation on a point (x, y)?

Back

The new coordinates after a 180° rotation about the origin are (-x, -y).

Front

Describe the transformation that occurs when a shape is reflected across the x-axis.

Back

When a shape is reflected across the x-axis, the y-coordinates of all points on the shape are inverted, resulting in new coordinates (x, -y).

Front

What is the difference between a rotation and a reflection?

Back

A rotation turns a shape around a point, while a reflection flips a shape over a line, creating a mirror image.