Dilations and Scale Factor

Front

What is a dilation in geometry?

Back

A dilation is a transformation that produces a figure similar to the original, but with a different size, using a scale factor.

Front

What does the scale factor indicate in a dilation?

Back

The scale factor indicates how much larger or smaller the dilated figure is compared to the original figure.

Front

If the scale factor is greater than 1, what happens to the figure?

Back

The figure enlarges.

Front

If the scale factor is between 0 and 1, what happens to the figure?

Back

The figure shrinks.

Front

What is the algebraic notation for a dilation with a scale factor of k?

Back

(x, y) goes to (kx, ky) where k is the scale factor.

Front

True or False: A dilation produces a congruent figure.

Back

False. A dilation produces a similar figure, not a congruent one.

Front

How do you find the coordinates of a dilated point A(x, y) with a scale factor of 3?

Back

Multiply both coordinates by 3: A' = (3x, 3y).

Front

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

Back

The scale factor is 1/4.

Front

If a shape is dilated by a scale factor of 2, what happens to its area?

Back

The area of the shape increases by a factor of 2^2 = 4.

Front

What is the scale factor from a small shape to a big shape if the big shape is twice the size of the small shape?

Back

The scale factor is 2.