Dilations

Front

What is a dilation in geometry?

Back

A dilation is a transformation that changes the size of a figure but not its shape. It involves a scale factor and a center of dilation.

Front

What is a scale factor in dilation?

Back

The scale factor is a number that describes how much a figure is enlarged or reduced during a dilation. A scale factor greater than 1 enlarges the figure, while a scale factor between 0 and 1 reduces it.

Front

If a triangle has vertices A(2, 3), B(4, 5), and C(6, 1), what are the coordinates of A' after a dilation by a scale factor of 2?

Back

A' will be (4, 6).

Front

What happens to the coordinates of a point (x, y) when it is dilated by a scale factor of k?

Back

The new coordinates will be (kx, ky).

Front

If triangle ABC is dilated by a scale factor of 1/2, what happens to its area?

Back

The area of the triangle will be reduced to 1/4 of its original area.

Front

What is the center of dilation?

Back

The center of dilation is a fixed point in the plane about which all points are expanded or contracted during a dilation.

Front

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

Back

Multiply the original coordinates by the scale factor. For example, if the original point is (x, y) and the scale factor is k, the new point will be (kx, ky).

Front

What is the dilation rule for a scale factor of 3?

Back

The dilation rule is (x, y) → (3x, 3y).

Front

If a rectangle has vertices at (1, 1), (1, 3), (4, 1), and (4, 3), what are the new coordinates after a dilation by a scale factor of 2?

Back

The new coordinates will be (2, 2), (2, 6), (8, 2), and (8, 6).

Front

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

Back

A dilation with a scale factor of 1 leaves the figure unchanged.