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 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

How do you calculate the coordinates of a dilated point?

Back

To calculate the coordinates of a dilated point, multiply the original coordinates by the scale factor. If the center of dilation is the origin, for a point (x, y) and scale factor k, the new coordinates are (kx, ky).

Front

What happens to the shape of a figure during dilation?

Back

The shape of the figure remains the same during dilation; only the size changes.

Front

If a triangle has vertices at (2,0), (3,-1), and (-2,-5), what are the new coordinates after a dilation by a scale factor of 3?

Back

The new coordinates are (6,0), (9,-3), and (-6,-15).

Front

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

Back

A scale factor less than 1 reduces the size of the figure, making it smaller.

Front

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

Back

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

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 during the dilation.

Front

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

Back

If a figure is dilated by a scale factor of k, the area of the figure is multiplied by k². Therefore, a scale factor of 2 will quadruple the area.

Front

What is the relationship between the original figure and the dilated figure?

Back

The original figure and the dilated figure are similar; they have the same shape but different sizes.