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. The shape remains congruent and the distance and direction of the slide are defined by a vector.

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 (clockwise or counterclockwise).

Front

Explain reflection in geometric 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 is defined by a center point and a scale factor.

Front

What is the difference between congruent and similar figures?

Back

Congruent figures are identical in shape and size, while similar figures have the same shape but may differ in size. Similar figures have proportional corresponding sides.

Front

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

Back

To translate the point (x, y) by the vector (a, b), you add the vector components to the coordinates: (x + a, y + b).

Front

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

Back

A 90-degree rotation of the point (x, y) around the origin results in the new coordinates (-y, x).

Front

Describe the line of reflection for a shape.

Back

The line of reflection is the line over which a shape is flipped to create its mirror image. Each point on the original shape is equidistant from the line of reflection.

Front

What is the scale factor in dilation?

Back

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