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 point and a scale factor.

Front

What is a scale factor in dilations?

Back

The scale factor is a number that describes how much a figure is enlarged or reduced during a dilation. A scale factor greater than 1 indicates enlargement, while a scale factor between 0 and 1 indicates reduction.

Front

If a point (x, y) is dilated with a scale factor r, what are the new coordinates?

Back

The new coordinates will be (rx, ry).

Front

What happens to the coordinates of a point when the scale factor is 1?

Back

The coordinates remain unchanged; the image is congruent to the original.

Front

What is the effect of a negative scale factor in a dilation?

Back

A negative scale factor not only changes the size of the figure but also reflects it across the center of dilation.

Front

How do you find the scale factor when given the original and dilated points?

Back

The scale factor can be found by dividing the coordinates of the dilated point by the corresponding coordinates of the original point.

Front

What is the coordinate of the image of point B (4,9) under a dilation with center at the origin and scale factor r = 2?

Back

(8, 18) - The coordinates are multiplied by the scale factor.

Front

If triangle ABC is dilated using the rule (x, y)→(2x, 2y), what happens to the coordinates of point C (6, -3)?

Back

The new coordinates of C' will be (12, -6).

Front

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

Back

The scale factor is ¼.

Front

True or False: When a dilation has a scale factor greater than one, the dilation is an enlargement.

Back

True.