Rigid Transformation Sequences

Front

What is a rigid transformation?

Back

A rigid transformation is a transformation that preserves the shape and size of a figure. Examples include translations, reflections, and rotations.

Front

Define translation in the context of rigid transformations.

Back

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

Front

What is a reflection in geometry?

Back

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

Front

Explain rotation in rigid transformations.

Back

Rotation is a rigid transformation that turns a figure around a fixed point, known as the center of rotation, by a certain angle.

Front

What does it mean for two figures to be congruent?

Back

Two figures are congruent if they have the same shape and size, which can be achieved through rigid transformations.

Front

How do you perform a translation of a point?

Back

To translate a 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 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 happens to a point when it is rotated 90 degrees clockwise around the origin?

Back

Rotating a point (x, y) 90 degrees clockwise around the origin results in the point (y, -x).

Front

Describe the sequence of transformations: Reflect across the x-axis, then translate up.

Back

First, reflect the figure over the x-axis, then move the reflected figure upwards by a specified distance.

Front

What is the result of applying the transformation (x, y) → (-x, -y) to the point A(-1, -4)?

Back

The result is the point A' at (1, 4).