Unit Two: Dilations

Front

What is a dilation in geometry?

Back

A dilation is a transformation that alters the size of a figure but preserves its shape. It is defined by a center point and 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. It determines how much larger or smaller the figure will become.

Front

What happens to a figure when the scale factor is greater than 1?

Back

When the scale factor is greater than 1, the figure enlarges.

Front

What happens to a figure when the scale factor is between 0 and 1?

Back

When the scale factor is between 0 and 1, the figure reduces in size.

Front

What happens to a figure when the scale factor is equal to 1?

Back

When the scale factor is equal to 1, the figure remains the same size.

Front

How do you perform a dilation on a point (x, y) using a scale factor k?

Back

To perform a dilation on a point (x, y) using a scale factor k, you multiply the coordinates by k: (x, y) → (kx, ky).

Front

What is the dilation rule for enlarging a shape by a scale factor of 8?

Back

The dilation rule for enlarging a shape by a scale factor of 8 is: (x, y) → (8x, 8y).

Front

What is the dilation rule for reducing a shape by a scale factor of 0.9?

Back

The dilation rule for reducing a shape by a scale factor of 0.9 is: (x, y) → (0.9x, 0.9y).

Front

If a shape is dilated with a scale factor of 5, what happens to its area?

Back

If a shape is dilated with a scale factor of 5, its area increases by a factor of 5² = 25.

Front

What is the effect of a negative scale factor on a dilation?

Back

A negative scale factor not only changes the size of the figure but also reflects it across the center point.