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.

Front

What are the four main types of transformations?

Back

The four main types of transformations are translation, rotation, reflection, and dilation.

Front

Define translation in geometry.

Back

Translation is a transformation that moves every point of a shape the same distance in a given direction.

Front

What is the effect of a translation of (x + a, y + b)?

Back

It moves the shape 'a' units horizontally and 'b' units vertically.

Front

How do you perform a rotation of a point around the origin?

Back

To rotate a point (x, y) around the origin by an angle θ, use the formulas: (x', y') = (x*cos(θ) - y*sin(θ), x*sin(θ) + y*cos(θ)).

Front

What is a reflection in geometry?

Back

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

Front

What is the line of reflection?

Back

The line of reflection is the line over which a shape is reflected to create a mirror image.

Front

Define dilation in geometry.

Back

Dilation is a transformation that changes the size of a shape but not its shape, using a scale factor.

Front

What is the scale factor in dilation?

Back

The scale factor is the ratio of the size of the image to the size of the original shape.

Front

How do you translate a point (x, y) by (3, 4)?

Back

Add 3 to the x-coordinate and 4 to the y-coordinate: (x + 3, y + 4).