Dilations

Front

What is a dilation in geometry?

Back

A dilation is a transformation that changes the size of a figure but not its shape, using 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.

Front

If a point (x, y) is dilated by a scale factor of k, what are the new coordinates?

Back

The new coordinates are (kx, ky).

Front

What happens to the coordinates of a point when it is dilated by a scale factor greater than 1?

Back

The coordinates of the point increase, making the figure larger.

Front

What happens to the coordinates of a point when it is dilated by a scale factor between 0 and 1?

Back

The coordinates of the point decrease, making the figure smaller.

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 if two figures are similar after a dilation?

Back

Two figures are similar if they have the same shape but different sizes, which is true for all dilations.

Front

What is the result of dilating a figure by a scale factor of 1?

Back

The figure remains unchanged; it is congruent to the original.

Front

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

Back

The new coordinates are (2, 4), (6, 8), and (10, 12).

Front

What does it mean for a shape to be congruent?

Back

Congruent shapes are identical in shape and size; they can be superimposed on each other.