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 scale factor and a center of dilation.

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 coordinates of a dilated point?

Back

To find the coordinates of a dilated point, multiply the original coordinates by the scale factor if the center of dilation is at the origin.

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 triangle is dilated by a scale factor of 2, what happens to its area?

Back

The area of the triangle is multiplied by the square of the scale factor, so it becomes 4 times larger.

Front

What is the algebraic rule for a dilation with a scale factor of k?

Back

The algebraic rule for a dilation with a scale factor of k is f(x, y) → (kx, ky).

Front

How do you find the new coordinates of a point after dilation?

Back

Multiply each coordinate of the original point by the scale factor.

Front

What happens to the distances between points during a dilation?

Back

The distances between points are multiplied by the scale factor during a dilation.

Front

If a point (x, y) is dilated by a scale factor of 1, what are the new coordinates?

Back

The new coordinates remain the same: (x, y).

Front

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

Back

A scale factor less than 1 reduces the size of the figure.