Dilations and Scale Factors

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 center of dilation 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. A scale factor greater than 1 enlarges the figure, while a scale factor between 0 and 1 reduces it.

Front

If a triangle with vertices (2,4), (4,2), (6,6) is dilated by a scale factor of 2 from the origin, what are the new vertices?

Back

The new vertices are (4,8), (8,4), (12,12).

Front

How do you dilate a point (x,y) by a scale factor k?

Back

To dilate a point (x,y) by a scale factor k, multiply both coordinates by k: (kx, ky).

Front

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

Back

When the scale factor is less than 1, the figure is reduced in size.

Front

What is the center of dilation?

Back

The center of dilation is the fixed point in the plane about which all points are expanded or contracted during a dilation.

Front

If point B is at (0,4) and is dilated by a scale factor of 3, what are the new coordinates?

Back

The new coordinates are (0,12).

Front

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

Back

A scale factor of 1 means the figure remains the same size; it is neither enlarged nor reduced.

Front

Back

The area of the rectangle is reduced to one-fourth of its original area because area scales by the square of the scale factor.

Front

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

Back

If the scale factor is greater than 1, it is an enlargement; if it is between 0 and 1, it is a reduction.