Dilation BASICS

Front

What is dilation in geometry?

Back

Dilation is a transformation that alters the size of a figure but keeps its shape the same. 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 scales, or multiplies, the dimensions of a figure during dilation. A scale factor greater than 1 enlarges the figure, while a scale factor between 0 and 1 reduces it.

Front

If a point A(2, 3) is dilated by a scale factor of 2, what are the coordinates of the image A'?

Back

A'(4, 6) - Each coordinate is multiplied by the scale factor.

Front

What happens to the shape of a figure during dilation?

Back

The shape of the figure remains the same; only the size changes.

Front

What is the center of dilation?

Back

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

Front

If B(5, 3) under a dilation has an image B'(20, 12), what is the scale factor?

Back

The scale factor is 4, calculated as k = (20/5) = 4.

Front

What is the difference between enlargement and reduction in dilation?

Back

Enlargement occurs when the scale factor is greater than 1, while reduction occurs when the scale factor is between 0 and 1.

Front

Which of the following is a scale factor for an enlargement? 1, 0.5, 2, 0.75

Back

2 - A scale factor greater than 1 indicates an enlargement.

Front

If a triangle has vertices at (1, 2), (3, 4), and (5, 6), and is dilated by a scale factor of 1/2, what are the new coordinates?

Back

(0.5, 1), (1.5, 2), (2.5, 3) - Each coordinate is multiplied by 1/2.

Front

What is the formula for finding the image of a point (x, y) after dilation?

Back

The image of a point (x, y) after dilation with scale factor k is given by (kx, ky).