Dilations

Front

What is a dilation in geometry?

Back

A dilation is a transformation that alters the size of a figure but maintains its shape, using a center of dilation and a scale factor.

Front

What is the center of dilation?

Back

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

Front

What does a scale factor greater than 1 indicate in a dilation?

Back

A scale factor greater than 1 indicates that the figure is enlarged.

Front

What does a scale factor less than 1 indicate in a dilation?

Back

A scale factor less than 1 indicates that the figure is reduced.

Front

If the center of dilation is at the origin, how do you find the coordinates of the dilated point?

Back

Multiply the original coordinates by the scale factor.

Front

What is the algebraic rule for a dilation with a scale factor of 2?

Back

If the center of dilation is at the origin, the rule is @@f(x,y) ightarrow (2x, 2y)@@.

Front

How do you determine the scale factor from two similar figures?

Back

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

Front

What happens to the angles of a figure during dilation?

Back

The angles of a figure remain unchanged during dilation.

Front

If triangle ABC is dilated by a scale factor of 3, what happens to the area of triangle ABC?

Back

The area of triangle ABC is multiplied by the square of the scale factor, so it becomes 9 times larger.

Front

What is the effect of a scale factor of 1 on a figure?

Back

A scale factor of 1 means the figure remains the same size; it is not altered.