Transformations - Rigid Motions

Front

What is a translation in geometry?

Back

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

Front

What does it mean to reflect a point across the y-axis?

Back

Reflecting a point across the y-axis means to create a mirror image of the point on the opposite side of the y-axis, changing the sign of the x-coordinate.

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

How do you describe a translation mathematically?

Back

A translation can be described using a vector, such as T(x, y) = (x + a, y + b), where (a, b) is the translation vector.

Front

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

Back

The new coordinates after a 90-degree clockwise rotation are (y, -x).

Front

What happens to the coordinates of a point when it is reflected across the x-axis?

Back

When a point (x, y) is reflected across the x-axis, its new coordinates become (x, -y).

Front

What is the result of translating the point (2, 3) by the vector (4, -1)?

Back

The new coordinates after the translation are (2 + 4, 3 - 1) = (6, 2).

Front

How do you find the image of a point after a reflection across the y-axis?

Back

To find the image of a point (x, y) after reflection across the y-axis, change the sign of the x-coordinate: the image is (-x, y).

Front

What is the formula for a translation that moves a point left by 3 and up by 2?

Back

The translation can be expressed as T(x, y) = (x - 3, y + 2).

Front

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

Back

The new coordinates after a 180-degree rotation are (-x, -y).