Sequence of Transformations with Dilations

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 larger or smaller the image will be compared to the original figure. 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 2, what happens to its coordinates?

Back

Each coordinate of the figure is multiplied by 2. For example, a point (x, y) becomes (2x, 2y).

Front

What is the center of dilation?

Back

The center of dilation is a fixed point in the plane about which all points of the figure are expanded or contracted.

Front

How do you determine if two figures are similar?

Back

Two figures are similar if one can be obtained from the other through a series of transformations including dilation, rotation, reflection, or translation.

Front

What is the effect of a dilation with a scale factor of 1?

Back

A dilation with a scale factor of 1 results in no change; the figure remains the same size.

Front

What is the transformation rule for a dilation with a scale factor of 0.5?

Back

The transformation rule is (x, y) → (0.5x, 0.5y), which reduces the size of the figure by half.

Front

What is the relationship between similar triangles and dilations?

Back

Similar triangles can be obtained from one another through dilation, meaning their corresponding angles are equal and their sides are in proportion.

Front

What is a rotation in geometry?

Back

A rotation is a transformation that turns a figure around a fixed point, known as the center of rotation, by a specified angle.

Front

What is the effect of a 90-degree rotation on a point (x, y)?

Back

A 90-degree rotation counterclockwise transforms the point (x, y) to (-y, x).