Dilation & Scale Factor

Dilation is a transformation that alters the size of a figure but maintains its shape, using a scale factor.

A scale factor is a number that scales, or multiplies, the dimensions of a figure during a dilation. It can be greater than 1 (enlargement) or less than 1 (reduction).

If the scale factor is greater than 1, it is an enlargement. If the scale factor is less than 1, it is a reduction.

The formula for scale factor is \( \frac{new}{old} \).

The new coordinates will be (1, 1.5), (2, 2.5), and (3, 3.5).

The area of the figure is multiplied by \( k^2 \).

The new figure is three times larger in each dimension compared to the original figure.

A scale factor of 1 means the figure remains the same size; there is no change.

To find the new coordinates after dilation, multiply each coordinate of the original point by the scale factor.

Two figures are similar if they have the same shape but may differ in size, typically achieved through dilation.