Transformations - Isometries

Front

What is an isometry in geometry?

Back

An isometry is a transformation that preserves distances and angles, meaning the original figure and its image are congruent.

Front

What are the four main types of isometries?

Back

The four main types of isometries are translations, rotations, reflections, and glide reflections.

Front

How does a reflection transformation work?

Back

A reflection transformation flips a figure over a line (the line of reflection), creating a mirror image.

Front

What is the effect of reflecting a point across the x-axis?

Back

Reflecting a point (x, y) across the x-axis results in the point (x, -y).

Front

What is the effect of reflecting a point across the y-axis?

Back

Reflecting a point (x, y) across the y-axis results in the point (-x, y).

Front

What is the result of a 90-degree rotation counterclockwise around the origin for the point (x, y)?

Back

The result is the point (-y, x).

Front

What is the result of a 180-degree rotation around the origin for the point (x, y)?

Back

The result is the point (-x, -y).

Front

What does it mean for two geometric figures to be congruent?

Back

Two geometric figures are congruent if they have the same size and shape.

Front

How do you find the image of a point after a reflection over the line y = k?

Back

To find the image of a point (x, y) after reflection over the line y = k, use the formula: (x, 2k - y).

Front

What is the composition of transformations?

Back

The composition of transformations is the application of two or more transformations in sequence to a figure.