Understanding Dilations in Geometry

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 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

How do you dilate a point (x, y) by a scale factor k?

Back

To dilate a point (x, y) by a scale factor k, multiply both coordinates by k: (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 will increase, resulting in an enlargement of the figure.

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 will decrease, resulting in a reduction of the figure.

Front

If point B(2, 3) is dilated by a scale factor of 2, what are the new coordinates?

Back

B'(4, 6) because (2*2, 3*2) = (4, 6).

Front

If point A(4, 5) is dilated by a scale factor of 1/2, what are the new coordinates?

Back

A'(2, 2.5) because (4*1/2, 5*1/2) = (2, 2.5).

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 find the scale factor when given the original and dilated points?

Back

The scale factor k can be found by dividing the distance from the center of dilation to the dilated point by the distance from the center to the original point.

Front

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

Back

A negative scale factor reflects the figure across the center of dilation in addition to resizing it.