3.5 and 3.6 Study Guide Practice

Front

What is dilation in geometry?

Back

Dilation is a transformation that alters the size of a figure but maintains its shape. It is defined by a scale factor that determines how much the figure is enlarged or reduced.

Front

What is the scale factor in dilation?

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 enlarges the figure, while a scale factor between 0 and 1 reduces it.

Front

If a figure is dilated by a scale factor of 3, what happens to its coordinates?

Back

Each coordinate (x, y) of the figure is multiplied by the scale factor. For a scale factor of 3, the new coordinates become (3x, 3y).

Front

How do you determine the coordinates of a dilated figure?

Back

To find the coordinates of a dilated figure, multiply each original coordinate by the scale factor. For example, if the original coordinates are (x, y) and the scale factor is k, the new coordinates will be (kx, ky).

Front

What does it mean for two figures to be similar?

Back

Two figures are similar if they have the same shape but not necessarily the same size. This means their corresponding angles are equal and their corresponding sides are proportional.

Front

What does it mean for two figures to be congruent?

Back

Two figures are congruent if they have the same shape and size. This means their corresponding sides and angles are equal.

Front

How do you write the algebraic notation for a dilation with a scale factor of 1/2?

Back

The algebraic notation for a dilation with a scale factor of 1/2 is (x, y) goes to (1/2x, 1/2y).

Front

If the coordinates of a point are (4, 6) and the scale factor is 2, what are the new coordinates after dilation?

Back

The new coordinates after dilation would be (8, 12) because each coordinate is multiplied by the scale factor: (2*4, 2*6).

Front

What is the relationship between congruence and similarity?

Back

All congruent figures are similar, but not all similar figures are congruent. Congruent figures have equal sides and angles, while similar figures have proportional sides and equal angles.

Front

How do you find the scale factor when given the coordinates of a dilated point?

Back

To find the scale factor, divide the coordinates of the dilated point by the corresponding coordinates of the original point. For example, if the original point is (x, y) and the dilated point is (x', y'), the scale factor k = x'/x = y'/y.