Dilations and other Transformations

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 indicate in a dilation?

Back

The scale factor indicates how much larger or smaller a figure will be after dilation. A scale factor greater than 1 enlarges the figure, while a scale factor less than 1 reduces it.

Front

If a triangle has vertices at (2, 3), (4, 5), and (6, 7), what are the coordinates after a dilation with a scale factor of 2?

Back

The new coordinates will be (4, 6), (8, 10), and (12, 14).

Front

What is the algebraic representation of a dilation with a scale factor of k?

Back

(x, y) → (kx, ky) where k is the scale factor.

Front

How do you find the center of dilation?

Back

The center of dilation is the point from which all points of the figure are expanded or contracted. It can be found by drawing lines from corresponding points of the original and dilated figures.

Front

What happens to the angles of a figure during dilation?

Back

The angles of a figure remain unchanged during dilation.

Front

If a figure is dilated by a scale factor of 1, what happens to the figure?

Back

The figure remains the same size; it is not altered.

Front

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

Back

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

Front

If quadrilateral ABCD is dilated by a scale factor of 1/2, what happens to its area?

Back

The area of the dilated figure will be 1/4 of the original area, since area scales by the square of the scale factor.

Front

What is the relationship between the original figure and the dilated figure?

Back

The original figure and the dilated figure are similar; they have the same shape but different sizes.