Dilations and Scale Factor

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 scale factor.

Front

What is a scale factor?

Back

The scale factor is a number that scales, or multiplies, the dimensions of a figure during a dilation.

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 area of a figure when it is dilated by a scale factor of k?

Back

The area is multiplied by the square of the scale factor, k^2.

Front

True or False: A dilation produces a congruent figure.

Back

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

Front

If a rectangle is dilated with a scale factor of 2, how does its perimeter change?

Back

The perimeter is also multiplied by 2.

Front

What is the scale factor if a triangle with vertices at (1, 1), (2, 2), and (3, 3) is dilated to (2, 2), (4, 4), and (6, 6)?

Back

The scale factor is 2.

Front

How do you find the scale factor when given two corresponding points, (x1, y1) and (x2, y2)?

Back

The scale factor is found by dividing the coordinates of the dilated point by the original point: k = (x2/x1) = (y2/y1).

Front

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

Back

A scale factor less than 1 reduces the size of the figure.

Front

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

Back

A scale factor greater than 1 enlarges the size of the figure.