Dilations and other transformations

Front

What is a dilation in geometry?

Back

A dilation is a transformation that alters the size of a figure but keeps its shape, defined by a scale factor.

Front

How do you write the algebraic notation for a dilation with a scale factor of 1/2?

Back

(x, y) → (1/2x, 1/2y)

Front

What does a scale factor of less than one indicate?

Back

It indicates that the image will be a reduction of the pre-image.

Front

If the point (8, 12) is dilated to (2, 3), what is the scale factor?

Back

1/4

Front

What is the scale factor for the transformation (x, y) → (2.5x, 2.5y)?

Back

2.5

Front

What is the effect of a scale factor greater than 1 on a figure?

Back

It enlarges the figure.

Front

What happens to the coordinates of a point (x, y) when it is dilated by a scale factor of 3?

Back

The new coordinates will be (3x, 3y).

Front

What is the formula for finding the scale factor when given two points before and after dilation?

Back

Scale Factor = (New Coordinate) / (Original Coordinate) for each corresponding coordinate.

Front

If a figure is dilated by a scale factor of 1, what happens to the figure?

Back

The figure remains unchanged.

Front

What is the relationship between the pre-image and image in a dilation?

Back

The image is a scaled version of the pre-image, maintaining the same shape.