Introduction
Dilation and rigid transformation are the transformation of objects and images. Rigid transformation changes the position and orientation of the image, while the dilation only changes the size of the object. In this article, you will learn more about transformation of geometric shapes.
Rigid Transformation
The rigid transformation is a transformation of an image or object that moves it from pre-image to new image by changing its position and orientation. The new transformed image will be congruent to the pre-image with the same size.
There are three common types of rigid transformation that are reflection, rotation and translation. All of these types of transformation preserve the size and shape of the objects. However, the direction and position may change.
Dilation
It is a process of transforming an object or any geometrical image without changing its shape and orientation with respect to a fixed origin. This fixed origin is known as the center of dilation.
Dilation of an image can reduce or expand its size in two-dimension. It depends on the dilation scale factor that is responsible for reduction or contraction of any object. The scale factor can be calculated by dividing the new image size with the dilation calculator on the pre-image size. The formula is:
$$(\text{Scale Factor})k\;=\;\frac{\text{new image size}}{\text{pre - image size}}$$
Is Dilation a Rigid Transformation?
The dilation is a transformation of an object by changing its size. Whereas in the rigid transformation, an object is transformed by changing its position and orientation. This transformation can be rotational or translational. Therefore, a dilation cannot be termed a rigid transformation.
There are some major differences between a dilation and a rigid transformation, which are explained in a difference table below.
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Dilation
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Rigid Transformation
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It is a transformation of an object that increases or decreases its size.
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It is a transformation that moves an object without increasing or decreasing its size.
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The position and orientation remain the same.
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The position and orientation does not remain the same.
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Pre-image and the new image formed by dilation are not congruent.
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Pre-image and the new image formed by rigid transformation are congruent.
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Dilation can only do reduction or contraction of an object’s size.
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Rigid transformation can form rotation, translation and reflection of an object.
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Properties of Dilation
Dilation has the following properties that make it differ from rigid transformation.
- The position and orientation remain the same.
- The preimage and new image have the same shape, but not the same size.
- Parallel lines move to parallel lines.
- The ratios of corresponding line segments are equal.
- Angles are moved to angles of the same measure.
Properties of Rigid Transformation
The rigid transformation has the following properties.
- The length of line segments remains the same.
- The size of the preimage and new image have the same size and shape.
- The angle of the preimage and new image remains the same.
- The orientation of the image does not remain the same.
How can Dilations be used in Real Life?
Dilations in math and geometry in both fields, have practical applications in various real-life scenarios. Here are some examples:
- Eye exams: In optometry, dilation is used to enlarge the pupil of the eye, allowing the eye doctor to better examine the structures inside the eye.
- Crime investigation: Detectives may use dilation techniques on pictures or surveillance footage to zoom in and gather finer details about evidence, such as fingerprints or facial features.
- Graphic designing: Dilations play a role in graphic design when resizing pictures, icons, or logos to fit specific spaces or maintain consistent proportions across different platforms or mediums.
In these real-life examples, dilation is utilized to enhance visibility, gather details, and ensure proper sizing, scaling of visual elements and transform the object size.
FAQ’s
Is Dilation a Rigid Motion?
No, dilation is not a rigid motion. The rigid motion is a transformation that moves a picture but does not change its size. But the dilation is the transformation of an object that changes its size without moving it.
Are all Dilations Congruent?
No, dilations are not congruent. In this transformation, an image can be reduced or expanded by its size. Both pre-image and new image are of the same shape with different sizes. Therefore, they are not congruent because they are the same shape but have not the same size.
Can Dilation be Negative?
Yes, it can be negative, but note that the negative dilation only does a reverse increment or decrement in the image size. It just explains the direction and position of an object.