Properties of Dilations

Front

What is a dilation in geometry?

Back

A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. It is defined by a center of dilation and a scale factor.

Front

What does a scale factor between 0 and 1 indicate in a dilation?

Back

A scale factor between 0 and 1 indicates a contraction, meaning the image will be smaller than the original.

Front

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

Back

A scale factor greater than 1 indicates an expansion, meaning the image will be larger than the original.

Front

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

Back

The new point is (kx, ky).

Front

What happens to the angles of a shape during a dilation?

Back

The corresponding angles of the original shape and the dilated shape remain equal.

Front

If polygon ABC is dilated by a scale factor of 2, what can be said about the new polygon A'B'C'?

Back

Polygon A'B'C' will be an enlargement of polygon ABC and will be proportional to it.

Front

What is the scale factor if the point (8, 12) is dilated to (2, 3)?

Back

The scale factor is 1/4.

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.

Front

If a dilation has a scale factor of 3, what is the effect on the original shape?

Back

The original shape will be enlarged by a factor of 3.

Front

What is the relationship between the original shape and the dilated shape in terms of similarity?

Back

The original shape and the dilated shape are similar, meaning they have the same shape but different sizes.