Dilations

Front

What is a dilation in geometry?

Back

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

Front

What does the scale factor in a dilation represent?

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 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 happens to the angles of a polygon during a dilation?

Back

The corresponding angles of the original polygon and the dilated polygon remain equal.

Front

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

Back

The area of the rectangle is reduced to 1/4 of its original area because area is proportional to the square of the scale factor.

Front

What is the dilation rule for a scale factor of 3 applied to the point (1, 2)?

Back

The new coordinates will be (3, 6) because (1, 2) becomes (3*1, 3*2).

Front

What is the difference between enlargement and reduction in dilations?

Back

Enlargement occurs when the scale factor is greater than 1, while reduction occurs when the scale factor is between 0 and 1.

Front

If a point (x, y) is dilated using the rule (x, y)→(kx, ky), what does k represent?

Back

The variable k represents the scale factor of the dilation.

Front

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

Back

A dilation with a scale factor of 1 leaves the figure unchanged in size.

Front

How do you determine if two polygons are similar after a dilation?

Back

Two polygons are similar if their corresponding angles are equal and the lengths of their corresponding sides are proportional.