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 of dilation and a scale factor.

Front

What does the scale factor (k) indicate in a dilation?

Back

The scale factor indicates how much the figure is enlarged or reduced. A scale factor greater than 1 enlarges the figure, while a scale factor less than 1 reduces it.

Front

If the scale factor is 2, what happens to the coordinates of a point (x, y) after dilation?

Back

The new coordinates will be (2x, 2y).

Front

What are the coordinates of the image of point A(3, 3) after a dilation with a scale factor of 3?

Back

A' (9, 9).

Front

What happens to a figure when the scale factor is less than 1?

Back

The figure undergoes a reduction, making it smaller.

Front

If point G(-10, -6) is dilated by a scale factor of 1/2, what are the new coordinates?

Back

G' (-5, -3).

Front

Is a dilation only an enlargement?

Back

No, a dilation can be both an enlargement and a reduction depending on the scale factor.

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

If a figure is dilated by a scale factor of 4, what happens to its area?

Back

The area of the figure is multiplied by the square of the scale factor, so it becomes 16 times larger.

Front

What is the effect of a scale factor of 1 on a figure?

Back

A scale factor of 1 means the figure remains unchanged in size.