What effect does dilation have on a geometric shape?

What effect does dilation have on a geometric shape?

• A. A dilation rotates the shape
• B. A dilation enlarges or reduces the shape proportionally
• C. A dilation reflects the shape across an axis
• D. A dilation skews the shape

Answer: (B)

Dilation is a transformation that alters the size of a geometric shape while maintaining the same proportions and shape. This means that every point of the shape moves away from or towards a fixed center point, known as the center of dilation, by a certain scale factor. If the scale factor is greater than one, the shape enlarges, and if the scale factor is less than one, the shape reduces in size. However, regardless of whether the shape is enlarged or reduced, the angles and the overall shape remain congruent to the original figure. This proportional change is a key characteristic of dilation. In contrast, other transformations mentioned, such as rotation, reflection, or skewing, alter the shape in ways that do not preserve its proportions or angles. For instance, rotation turns the shape around a center point, reflection flips it over an axis, and skewing distorts it without necessarily keeping the angles consistent. Thus, the nature of dilation specifically involves proportional enlargement or reduction, making it distinct from these other transformations.

Dilation is a transformation that alters the size of a geometric shape while maintaining the same proportions and shape. This means that every point of the shape moves away from or towards a fixed center point, known as the center of dilation, by a certain scale factor. If the scale factor is greater than one, the shape enlarges, and if the scale factor is less than one, the shape reduces in size. However, regardless of whether the shape is enlarged or reduced, the angles and the overall shape remain congruent to the original figure. This proportional change is a key characteristic of dilation.

In contrast, other transformations mentioned, such as rotation, reflection, or skewing, alter the shape in ways that do not preserve its proportions or angles. For instance, rotation turns the shape around a center point, reflection flips it over an axis, and skewing distorts it without necessarily keeping the angles consistent. Thus, the nature of dilation specifically involves proportional enlargement or reduction, making it distinct from these other transformations.