Dilations

Front

What is a dilation in geometry?

Back

A dilation is a transformation that produces a figure similar to the original by enlarging or reducing it, using a center of dilation and a scale factor.

Front

What does the scale factor (k) indicate in a dilation?

Back

The scale factor (k) indicates how much the figure is enlarged or reduced. If k > 1, the figure is enlarged; if k < 1, the figure is reduced; if k = 1, the figure remains the same size.

Front

What is the effect of a scale factor of 1/2 on a figure?

Back

A scale factor of 1/2 reduces the size of the figure to half of its original dimensions.

Front

What happens to the coordinates of a point (x, y) after a dilation with center at the origin and scale factor k?

Back

The new coordinates will be (kx, ky).

Front

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

Back

A'(6,0), B'(9,-3), C'(-6,-15).

Front

True or False: A dilation produces a congruent figure.

Back

False. A dilation produces a similar figure, not necessarily congruent.

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

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

Back

Multiply each coordinate of the point by the scale factor.

Front

What is the scale factor if a figure is reduced to 1/4 of its original size?

Back

The scale factor is 1/4.

Front

If the scale factor is greater than 1, what type of transformation occurs?

Back

The figure is enlarged.