Multiple Transformations

Front

What is a translation in geometry?

Back

A translation is a transformation that moves every point of a figure the same distance in a specified direction.

Front

How do you perform a translation of a point (x, y) by (a, b)?

Back

To translate the point (x, y) by (a, b), you add a to the x-coordinate and b to the y-coordinate, resulting in (x + a, y + b).

Front

What is a reflection in geometry?

Back

A reflection is a transformation that flips a figure over a line, creating a mirror image.

Front

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

Back

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

Front

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

Back

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

Front

What is a rotation in geometry?

Back

A rotation is a transformation that turns a figure around a fixed point, known as the center of rotation, by a specified angle.

Front

What are the coordinates of a point after a 180° rotation about the origin?

Back

After a 180° rotation about the origin, the coordinates of a point (x, y) become (-x, -y).

Front

What is the line of reflection for a reflection over the line y = -x?

Back

The line of reflection y = -x swaps the x and y coordinates of a point, resulting in the point (y, x).

Front

What is the combined effect of a reflection across the x-axis followed by a reflection across the y-axis?

Back

The combined effect of these two reflections is equivalent to a rotation of 180° about the origin.

Front

How do you write a rule for a translation?

Back

A rule for a translation can be written as (x + a, y + b), where a is the horizontal shift and b is the vertical shift.