Transformations - Isometries

Front

What is an isometry?

Back

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

Front

What are the types of isometries?

Back

The types of isometries include translations, rotations, reflections, and glide reflections.

Front

How do you perform a translation on a point?

Back

To translate a point, you add specific values to the x and y coordinates of the point.

Front

What is the result of reflecting a point over the x-axis?

Back

The y-coordinate of the point changes sign, while the x-coordinate remains the same.

Front

What happens to the coordinates of a point (x, y) when it is reflected over the line y = k?

Back

The new coordinates will be (x, 2k - y).

Front

What is the effect of a reflection over the y-axis on the point (x, y)?

Back

The new coordinates will be (-x, y).

Front

How do you find the image of a point after a translation?

Back

Add the translation vector to the original coordinates of the point.

Front

What does it mean for two figures to be congruent?

Back

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

Front

How do you reflect a point over the line y = -2?

Back

To reflect a point (x, y) over the line y = -2, calculate the new y-coordinate as -2 - (y + 2).

Front

What is the formula for a translation of a point (x, y) by (a, b)?

Back

The new coordinates will be (x + a, y + b).