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 scale factor in a dilation?

Back

The scale factor is a number that describes how much a figure is enlarged or reduced during a dilation.

Front

How do you determine 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 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 coordinates of a point when the scale factor is greater than 1?

Back

The coordinates of the point will increase, resulting in a larger figure.

Front

What happens to the coordinates of a point when the scale factor is between 0 and 1?

Back

The coordinates of the point will decrease, resulting in a smaller figure.

Front

What is the effect of a negative scale factor in dilation?

Back

A negative scale factor not only changes the size but also reflects the figure across the center of dilation.

Front

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

Back

The scale factor can be found by dividing the distance from the center of dilation to the dilated point by the distance from the center to the original point.

Front

If quadrilateral ABCD is dilated to A'B'C'D' with a scale factor of 2, what can you say about the lengths of the sides?

Back

The lengths of the sides of A'B'C'D' will be twice the lengths of the corresponding sides of ABCD.

Front

What is the relationship between the area of a figure and the scale factor in dilation?

Back

The area of a figure is multiplied by the square of the scale factor during dilation.