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 keeps its shape the same. 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. A scale factor greater than 1 enlarges the figure, while a scale factor between 0 and 1 reduces it.

Front

If a point (x, y) is dilated from the origin by a scale factor of k, what are the new coordinates?

Back

The new coordinates will be (kx, ky).

Front

What happens to the coordinates of a triangle when it is dilated by a scale factor of 3?

Back

Each coordinate of the triangle's vertices is multiplied by 3.

Front

If a rectangle with vertices at (1, 1), (4, 1), (4, 3), and (1, 3) is dilated by a scale factor of 1/2, what are the new coordinates of the vertex (4, 3)?

Back

The new coordinates will be (2, 1.5).

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 does not change.

Front

How do you determine the scale factor used in a dilation?

Back

The scale factor can be determined by comparing the lengths of corresponding sides of the original figure and the dilated figure.

Front

If triangle ABC is dilated by a scale factor of 1/2, what happens to the area of the triangle?

Back

The area of the triangle is reduced by a factor of (1/2)^2 = 1/4.

Front

What are the coordinates of the image of the point (2, 0) after a dilation by a scale factor of 3 from the origin?

Back

The coordinates will be (6, 0).

Front

If a figure is dilated by a scale factor of 2, how does this affect the perimeter?

Back

The perimeter of the figure is also multiplied by the scale factor, so it becomes twice as long.