12/5 Dilations Warm Up

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 scale factor and a center of dilation.

Front

What does the scale factor indicate in a dilation?

Back

The scale factor indicates how much larger or smaller the image will be compared to the original figure. A scale factor greater than 1 enlarges the figure, while a scale factor between 0 and 1 reduces it.

Front

If a figure is dilated by a scale factor of 3, what happens to its coordinates?

Back

Each coordinate (x, y) of the figure is multiplied by 3, resulting in new coordinates (3x, 3y).

Front

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

Back

A'(9,9) because (3*3, 3*3) = (9, 9).

Front

What happens to a polygon when it is dilated by a scale factor less than 1?

Back

The image of the polygon becomes smaller than the original polygon.

Front

What is the result of the dilation transformation (x, y) --> (2x, 2y)?

Back

This transformation doubles the size of the figure, making it larger.

Front

If a triangle is dilated by a scale factor of 2, how does its area change?

Back

The area of the triangle increases by a factor of 2^2 = 4.

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 during the dilation.

Front

How do you determine the image of a polygon after dilation?

Back

To find the image, multiply each vertex's coordinates by the scale factor.

Front

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

Back

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