Dilations

A transformation that resizes a geometric figure using a scale factor without changing its overall shape is called a _____

dilation

The fixed point from which a figure is enlarged or reduced during a transformation is called the center of _____

dilation

The ratio of a side length of the dilated image to the corresponding side length of the original figure is called the _____

scale factor

If a dilation has a scale factor $k$ where $k > 1$, the resulting transformation is an _____

enlargement

If a dilation has a scale factor $k$ where $0 < k < 1$, the resulting transformation is a _____

reduction

When dilating a coordinate point $(x, y)$ centered at the origin by a scale factor of $k$, the algebraic rule is $(x, y) \rightarrow$ _____

$$(kx, ky)$$

Dilating the point $(3, 5)$ centered at the origin with a scale factor of $k = 3$ results in the new coordinates _____

$$(9, 15)$$

Dilating the point $(8, 12)$ centered at the origin with a scale factor of $k = \frac{1}{4}$ results in the new coordinates _____

$$(2, 3)$$

A transformation that resizes a geometric figure using a scale factor without changing its overall shape is called a _____

dilation

The fixed point from which a figure is enlarged or reduced during a transformation is called the center of _____

dilation

The ratio of a side length of the dilated image to the corresponding side length of the original figure is called the _____

scale factor

If a dilation has a scale factor $k$ where $k > 1$, the resulting transformation is an _____

enlargement

If a dilation has a scale factor $k$ where $0 < k < 1$, the resulting transformation is a _____

reduction

When dilating a coordinate point $(x, y)$ centered at the origin by a scale factor of $k$, the algebraic rule is $(x, y) \rightarrow$ _____

$$(kx, ky)$$

Dilating the point $(3, 5)$ centered at the origin with a scale factor of $k = 3$ results in the new coordinates _____

$$(9, 15)$$

Dilating the point $(8, 12)$ centered at the origin with a scale factor of $k = \frac{1}{4}$ results in the new coordinates _____

$$(2, 3)$$

Two geometric figures that have the same shape but not necessarily the same size after a dilation are called _____ figures.

similar

Under a dilation, corresponding angle measures between the original figure and its image remain _____

congruent

If a dilation has a scale factor of $k = 1$, the resulting image is _____ to the original figure.

congruent

If point $P(4, 10)$ is dilated centered at the origin to produce $P'(2, 5)$, the scale factor $k$ is _____

$$\frac{1}{2}$$

A line segment that does not pass through the center of dilation produces an image segment that is _____ to the original line segment.

parallel