Transformations

Front

What is a transformation in geometry?

Back

A transformation in geometry is an operation that moves or changes a shape in some way to produce a new shape. The main types of transformations are translations, rotations, reflections, and dilations.

Front

Define translation in the context of transformations.

Back

Translation is a type of transformation that slides a shape from one position to another without turning it. Each point of the shape moves the same distance in the same direction.

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 specific direction.

Front

Explain reflection in transformations.

Back

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

Front

What is dilation in geometry?

Back

Dilation is a transformation that changes the size of a shape but keeps its proportions the same. It involves a center of dilation and a scale factor.

Front

What is the difference between rigid and non-rigid transformations?

Back

Rigid transformations (translations, rotations, reflections) preserve the shape and size of the figure, while non-rigid transformations (dilations) change the size but not the shape.

Front

How do you perform a translation on a point (3, 4) by the vector (2, -3)?

Back

To translate the point (3, 4) by the vector (2, -3), add the vector components to the point's coordinates: (3+2, 4-3) = (5, 1).

Front

What happens to the coordinates of a point (x, y) after a reflection over the x-axis?

Back

After reflecting a point (x, y) over the x-axis, the new coordinates will be (x, -y).

Front

How do you rotate a point (1, 0) 90 degrees counterclockwise around the origin?

Back

To rotate the point (1, 0) 90 degrees counterclockwise around the origin, the new coordinates will be (0, 1).

Front

What is the scale factor in a dilation?

Back

The scale factor in a dilation is a number that describes how much the shape is enlarged or reduced. A scale factor greater than 1 enlarges the shape, while a scale factor between 0 and 1 reduces it.