Dilations

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 center of dilation?

Back

The center of dilation is a fixed point in the plane about which all points are expanded or contracted.

Front

How do you determine the scale factor in a dilation?

Back

The scale factor is determined by the ratio of the distance from the center of dilation to a point and the distance from the center to the corresponding point after dilation.

Front

If the scale factor is greater than 1, what happens to the figure?

Back

If the scale factor is greater than 1, the figure enlarges.

Front

If the scale factor is between 0 and 1, what happens to the figure?

Back

If the scale factor is between 0 and 1, the figure shrinks.

Front

What is the algebraic rule for dilation with a scale factor of k?

Back

The algebraic rule for dilation with a scale factor of k is given by: @@f(x,y) ightarrow (kx, ky)@@.

Front

How do you find the coordinates of a dilated point?

Back

To find the coordinates of a dilated point, multiply the original coordinates by the scale factor and add the center of dilation if it is not the origin.

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.

Front

What is the relationship between the original point and the dilated point?

Back

The dilated point is located along the line that connects the center of dilation to the original point, at a distance scaled by the scale factor.

Front

How do you express the coordinates of a point after dilation?

Back