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, using a scale factor and a center of dilation.

Front

What is the scale factor in a dilation?

Back

The scale factor is a number that describes how much a figure is enlarged or reduced during a dilation.

Front

If a figure is dilated by a scale factor of 2, what happens to its dimensions?

Back

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

Front

What are the coordinates of a point (x, y) after dilation by a scale factor of k?

Back

The new coordinates will be (kx, ky).

Front

How do you find the scale factor when given the original and dilated points?

Back

The scale factor can be found by dividing the coordinates of the dilated point by the corresponding coordinates of the original point.

Front

What is the center of dilation?

Back

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

Front

If a triangle with vertices (1, 2), (3, 4), and (5, 6) is dilated by a scale factor of 3, what are the new coordinates?

Back

The new coordinates will be (3, 6), (9, 12), and (15, 18).

Front

What happens to the angles of a figure during dilation?

Back

The angles of a figure remain unchanged during a dilation.

Front

If a point (4, 8) is dilated to (1, 2), what is the scale factor?

Back

The scale factor is 1/4.

Front

How do you determine if two figures are similar after dilation?

Back

Two figures are similar if their corresponding angles are equal and their corresponding sides are in proportion.