transformations semester review

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. The main types of transformations are translations, rotations, reflections, and dilations.

Front

Define translation in geometry.

Back

Translation is a type of transformation that slides a shape from one position to another without turning it or flipping it.

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.

Front

Explain reflection in geometry.

Back

Reflection is a transformation that flips a shape over a line, 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.

Front

How do you perform a translation on a coordinate plane?

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 the new point (x+a, y+b).

Front

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

Back

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

Front

How do you reflect a point across the x-axis?

Back

To reflect a point (x, y) across the x-axis, the new coordinates become (x, -y).

Front

What is the scale factor in dilation?

Back

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