Dilations!

Front

What is a dilation in geometry?

Back

A dilation is a transformation that alters the size of a figure but keeps its shape, using a center point and a scale factor.

Front

What does the scale factor in a dilation represent?

Back

The scale factor indicates how much larger or smaller the image will be compared to the original figure.

Front

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

Back

An enlargement occurs.

Front

If the scale factor is less than 1, what type of dilation occurs?

Back

A reduction occurs.

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 image of a point (x, y) under a dilation with scale factor k?

Back

Multiply both coordinates by the scale factor: (kx, ky).

Front

What happens to the coordinates of a point (2, 3) under a dilation with a scale factor of 3?

Back

The new coordinates will be (6, 9).

Front

Is a dilation always an enlargement?

Back

No, a dilation can be either an enlargement or a reduction depending on the scale factor.

Front

What is the image of point B (4, 9) under a dilation with center at the origin and scale factor of 2?

Back

B' (8, 18).

Front

What is the image of point A (3, 3) under a dilation with a scale factor of 3?

Back

A' (9, 9).