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, either enlarging or reducing it.

Front

What does the scale factor indicate in a dilation?

Back

The scale factor indicates how much a figure is enlarged or reduced. A scale factor greater than 1 indicates enlargement, while a scale factor less than 1 indicates reduction.

Front

If a shape is dilated by a scale factor of 2, what happens to its size?

Back

The shape is enlarged to twice its original size.

Front

If a shape is dilated by a scale factor of 1/2, what happens to its size?

Back

The shape is reduced to half its original size.

Front

What is the new perimeter of a rectangle with an original perimeter of 30 cm when enlarged by a scale factor of 4?

Back

120 cm.

Front

What is the result of dilating a triangle with coordinates A(2, 3), B(4, 5), and C(6, 7) by a scale factor of 1/2?

Back

The new coordinates will be A(1, 1.5), B(2, 2.5), C(3, 3.5).

Front

What is the relationship between the original and new area of a shape when dilated by a scale factor of k?

Back

The new area is k^2 times the original area.

Front

If triangle ABC is dilated by a scale factor of 1/2, what will be the coordinates of point C if C is originally at (6, -3)?

Back

C' will be at (3, -1.5).

Front

What is the difference between enlargement and reduction in dilations?

Back

Enlargement increases the size of the figure (scale factor > 1), while reduction decreases the size (scale factor < 1).

Front

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

Back

Divide the length of a side of the larger figure by the corresponding side of the smaller figure.