Dilations and other Transformations

Front

What is a dilation in geometry?

Back

A dilation is a transformation that alters the size of a figure but maintains its shape. It is defined by 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. A scale factor greater than 1 enlarges the figure, while a scale factor between 0 and 1 reduces it.

Front

If triangle ABC has vertices A(2, 3), B(4, 5), and C(6, 7), what are the coordinates of B' after a dilation with a scale factor of 2 centered at the origin?

Back

B' would be at (8, 10) after applying the scale factor of 2.

Front

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

Back

The new coordinates will be (kx, ky).

Front

If triangle ABC is dilated to produce triangle A'B'C' with a scale factor of 3/4, what can we say about the size of triangle A'B'C'?

Back

Triangle A'B'C' is a reduction of triangle ABC.

Front

How do you find the new 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 center of dilation?

Back

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

Front

If a triangle is dilated by a scale factor of 1, what happens to the triangle?

Back

The triangle remains unchanged; it retains its original size and shape.

Front

What is the relationship between the original figure and its image after dilation?

Back

The original figure and its image are similar; they have the same shape but may differ in size.

Front

If triangle ABC is dilated by a scale factor of 3, what is the relationship between the lengths of the sides of triangle ABC and triangle A'B'C'?

Back

The lengths of the sides of triangle A'B'C' will be three times the lengths of the corresponding sides of triangle ABC.