Dilations

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 does a scale factor greater than 1 indicate in a dilation?

Back

A scale factor greater than 1 indicates an enlargement of the figure.

Front

What does a scale factor less than 1 indicate in a dilation?

Back

A scale factor less than 1 indicates a reduction of the figure.

Front

If a figure is dilated using the rule (x, y) → (kx, ky), what do k, x, and y represent?

Back

k is the scale factor, and x and y are the original coordinates of the points in the figure.

Front

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

Back

Compare the scale factor to 1: if it's greater than 1, it's an enlargement; if it's less than 1, it's a reduction.

Front

What are the coordinates of a point C(6, -3) after a dilation with a scale factor of 2?

Back

C' would be (12, -6) after the dilation.

Front

What is the effect of a scale factor of 1 on a figure during dilation?

Back

A scale factor of 1 means the figure remains unchanged in size.

Front

If triangle ABC is dilated to create triangle A'B'C' with a scale factor of 3/2, how does the size of triangle A'B'C' compare to triangle ABC?

Back

Triangle A'B'C' is larger than triangle ABC by a factor of 1.5.

Front

What is the formula for dilating a point (x, y) by a scale factor of k?

Back

The formula is (x, y) → (kx, ky).

Front

If a figure is dilated by a scale factor of 1/3, what happens to its area?

Back

The area of the figure is reduced by a factor of (1/3)² = 1/9.