Sequences of transformations

Front

What is a transformation in geometry?

Back

A transformation is an operation that moves or changes a shape in some way to produce a new shape. Common transformations include translations, rotations, reflections, and dilations.

Front

Define translation in the context of transformations.

Back

Translation is a type of transformation that slides a shape in a straight line from one position to another without changing its size, shape, or orientation.

Front

What is a rotation in geometry?

Back

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

Front

Explain reflection in geometric transformations.

Back

Reflection is a transformation that flips a shape over a line, creating a mirror image of the original shape.

Front

What does it mean to rotate a shape 90 degrees counterclockwise?

Back

Rotating a shape 90 degrees counterclockwise means turning the shape 90 degrees to the left around a fixed point, typically the origin.

Front

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

Back

To find the new coordinates after a translation, you add the translation values to the original coordinates. For example, translating a point (x, y) by (a, b) results in (x+a, y+b).

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). The x-coordinate remains the same while the y-coordinate changes sign.

Front

Describe the sequence of transformations: translation followed by reflection.

Back

In this sequence, the shape is first moved to a new position (translation) and then flipped over a line (reflection), resulting in a new orientation and position.

Front

What are the coordinates of a point after a 90-degree rotation about the origin?

Back

For a point (x, y), after a 90-degree rotation counterclockwise about the origin, the new coordinates will be (-y, x).

Front

How do you determine the final position of a shape after multiple transformations?

Back

To determine the final position, apply each transformation step-by-step to the original coordinates, updating the coordinates after each transformation.