Dilations & Scale Factor

Front

What is a dilation in geometry?

Back

A dilation is a transformation that alters the size of a figure but not its shape, using a scale factor.

Front

What is a scale factor?

Back

A scale factor is a number that scales, or multiplies, the dimensions of a figure during a dilation.

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 happens to the coordinates of a point (x, y) when it is dilated by a scale factor of 2?

Back

The new coordinates will be (2x, 2y).

Front

If a figure is dilated with a scale factor greater than 1, what type of transformation occurs?

Back

It is an enlargement.

Front

If a figure is dilated with a scale factor less than 1, what type of transformation occurs?

Back

It is a reduction.

Front

What is the result of dilating a triangle with vertices at (3, 2), (4, 5), and (5, 1) by a scale factor of 2?

Back

The new vertices will be (6, 4), (8, 10), and (10, 2).

Front

How do you determine if a dilation is an enlargement or a reduction?

Back

Compare the scale factor to 1: if > 1, it's an enlargement; if < 1, it's a reduction.

Front

What is the algebraic representation of a dilation with a scale factor of 3?

Back

(x, y) → (3x, 3y)