Unit 7 Flashcard #1: Dilations and Similarity

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 center of dilation and a scale factor.

Front

What does the scale factor in a dilation represent?

Back

The scale factor indicates how much the figure is enlarged or reduced. A scale factor greater than 1 enlarges the figure, while a scale factor between 0 and 1 reduces it.

Front

If the coordinates of point A are (x, y), what are the coordinates of point A' after a dilation with a scale factor k?

Back

The coordinates of point A' will be (kx, ky).

Front

What happens to the shape of a figure when the scale factor is 1?

Back

The figure remains unchanged in size and shape.

Front

How do you determine the coordinates of a point after dilation with the center of dilation at the origin?

Back

Multiply each coordinate of the point by the scale factor.

Front

What is the result of a dilation with a scale factor of 1/2 on the point (4, 6)?

Back

The new coordinates will be (2, 3).

Front

What is the relationship between similar figures?

Back

Similar figures have the same shape but may differ in size; their corresponding angles are equal and their corresponding sides are proportional.

Front

What is the scale factor if quadrilateral ABC is dilated to quadrilateral A'B'C' and the lengths of corresponding sides are in the ratio 1:2?

Back

The scale factor is 2.

Front

True or False: A dilation can change the angles of a figure.

Back

False. A dilation does not change the angles of a figure.

Front

What does it mean for two figures to be congruent?

Back

Two figures are congruent if they have the same shape and the same size.