Dilations

Front

What is a dilation in geometry?

Back

A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. It is defined by a center of dilation and a scale factor.

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. A scale factor greater than 1 enlarges the figure, while a scale factor between 0 and 1 reduces it.

Front

How do you find the coordinates of a dilated point?

Back

To find the coordinates of a point after dilation, multiply the coordinates of the original point by the scale factor and then add the coordinates of the center of dilation.

Front

What happens to the angles of a figure during a dilation?

Back

The angles of a figure remain unchanged during a dilation; they are congruent to the angles of the original figure.

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

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

Back

The area of the triangle is multiplied by the square of the scale factor. If the scale factor is 2, the area is multiplied by 2^2 = 4.

Front

True or False: A dilation always produces a congruent figure.

Back

False. A dilation produces a similar figure, which may be larger or smaller, but not congruent.

Front

What are similar figures?

Back

Similar figures are figures that have the same shape but may differ in size. They have proportional corresponding sides and equal corresponding angles.

Front

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

Back

For a point (x, y) and a scale factor k, the new coordinates after dilation are (kx, ky).

Front

What is the effect of a negative scale factor in dilation?

Back

A negative scale factor not only changes the size of the figure but also reflects it across the center of dilation.