Dilations Activity

Front

What is a dilation in geometry?

Back

A dilation is a transformation that alters the size of a figure but maintains its shape. It is defined by a center point and a scale factor.

Front

What does the scale factor in a dilation represent?

Back

The scale factor indicates how much larger or smaller a figure will be after the dilation. A scale factor greater than 1 enlarges the figure, while a scale factor between 0 and 1 reduces it.

Front

If a point A has coordinates (x, y), what are the coordinates of A' after a dilation with a scale factor k?

Back

The coordinates of A' will be (kx, ky).

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 during the dilation.

Front

How do you determine the new coordinates of a point after dilation?

Back

Multiply the original coordinates of the point by the scale factor.

Front

If the scale factor is 2 and the original point is (3, 4), what are the coordinates of the dilated point?

Back

The coordinates of the dilated point will be (6, 8).

Front

What happens to the distances between points during a dilation?

Back

The distances between points are multiplied by the scale factor during a dilation.

Front

If a triangle has vertices at (1, 2), (3, 4), and (5, 6), what are the new vertices after a dilation with a scale factor of 3?

Back

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

Front

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

Back

A scale factor of 1 means the figure remains unchanged in size.

Front

How do you find the image of a point under dilation with respect to a center of dilation?

Back

To find the image of a point, draw a line from the center of dilation to the point, then extend that line by the scale factor.