Dilation (Scale Factor)

Front

What is dilation in geometry?

Back

Dilation is a transformation that alters the size of a figure but not its shape. It involves a center of dilation and a scale factor.

Front

What is a 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 triangle is dilated with a scale factor of 2, what happens to its dimensions?

Back

Each dimension of the triangle is multiplied by 2, making the triangle twice as large.

Front

What is the algebraic representation of a dilation with a scale factor of 1/2?

Back

The algebraic representation is @@(x, y) ightarrow igg(rac{1}{2}x, rac{1}{2}yigg)@@.

Front

How do you determine the scale factor when comparing two similar figures?

Back

The scale factor can be determined by dividing the length of a side of the dilated figure by the corresponding side of the original figure.

Front

What is the center of dilation?

Back

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

Front

If triangle ABC is dilated to triangle A'B'C' with a scale factor of 3, what is the relationship between the sides of the triangles?

Back

The sides of triangle A'B'C' are three times the length of the corresponding sides of triangle ABC.

Front

What happens to the coordinates of a point (x, y) when it is dilated with a scale factor of 3?

Back

The new coordinates will be (3x, 3y).

Front

If a quadrilateral ABCD is dilated to A'B'C'D' with a scale factor of 1/3, what is the new area compared to the original area?

Back

The area of the dilated quadrilateral A'B'C'D' will be 1/9 of the area of quadrilateral ABCD.

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.