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 the same, using a center of dilation and a scale factor.

Front

What does the scale factor in a dilation represent?

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 between 0 and 1 reduces it.

Front

If a point (x, y) is dilated with a scale factor k, what are the new coordinates?

Back

The new coordinates will be (kx, ky).

Front

What happens to the angles of a shape during a dilation?

Back

The angles of the shape remain unchanged during a dilation.

Front

How do you find the scale factor when given the original and dilated coordinates?

Back

The scale factor can be found by dividing the coordinates of the dilated point by the corresponding coordinates of the original point.

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 point A(4, 6) is dilated by a scale factor of 1/2, what are the new coordinates?

Back

The new coordinates are (2, 3).

Front

True or False: A dilation can change the shape of a figure.

Back

False. A dilation does not change the shape, only the size.

Front

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

Back

A scale factor of 1 means the figure remains the same size; it does not change.

Front

If quadrilateral ABCD is dilated to A'B'C'D' with a scale factor of 3, how does the area change?

Back

The area of the dilated figure increases by a factor of 3^2 = 9.