Dilation: Definition, Scale Factor, Properties & Sample Questions

A dilation is a stretch or shrinkage of an image in geometry. By stretching, we mean to make something larger, and by shrinking, we mean to make something smaller. Stretching simply means making a larger proportional image of the original image while shrinking simply means making a smaller proportional image of the original image. It is important to note that, unlike other transformations, dilation does not result in a change in orientation or shape. There are four basic types of transformations in geometry. They are as follows: Translation, Rotation, Reflection, Resizing, or Dilation. Here, we will discuss more about dilation along with some important questions.

Read Also: Distance Formula of Coordinate Geometry

Key Takeaways: Dilation, Scale factor, Center of Dilation, Horizontal dilation, Vertical dilation

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Dilation with a Scale Factor

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A dilation is a transformation that yields a figure with the same shape as the original but not the same size. The scale factor is used for both enlargement and reduction.

For example, if you have a 6 x 4 photograph and want it enlarged to 12 x 8, you can do so. In order to do that, you must first determine the scale factor. What do we multiply this picture by to get this enlargement? There is a formula that we can use that works in any situation.

Scale factor = length of scale diagram/length of original diagram

= 12/6 =2

• If the scale factor is greater than one, the image will stretch.
• The image shrinks if the scale factor is between 0 and 1.
• If the scale factor is 1, the original and produced images are congruent.

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Dilation Center

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The point of reference in the center of dilation. Dilation changes the size of the figure, which can increase or decrease. The resizing takes place from a point known as the center of dilation. It is the dilation center from which the objects/figures expand or contract. Point O in the diagram is the center of dilation.

Dilation Center

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Definitions

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• A dilation is a transformation that enlarges or contracts the size of a figure. This means that the pre-image and image are similar and are scaled up or down using a scale factor. The original figure is stretched or shrunk as a result of dilation.
• The scale factor is the number multiplied by each coordinate to obtain the new image.
• The center of dilation is a fixed point in the plane.

Check Important Notes for Section Formula of Coordinate Geometry

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Properties of Dilation

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Some characteristics of shapes that remain unchanged during dilation transformations are:

• Each angle of the figure is the same
• Midpoints of the figure's sides remain the same as the midpoint of the dilated shape
• Parallel and perpendicular lines in the figure remain the same as the parallel and perpendicular lines of the dilated figure

The only thing that changes during the dilation process is the distance between the points. It means that the sides of the original image and the dilated image may differ in length. Dilation processes are classified into two types. They are as follows:

Horizontal Dilation- It is the process of stretching a function so that the distance from f(x) to the y-axis is increased by a factor.

A function y=f(x) is dilated horizontally by a scale factor C in the dilation transformation.

Y = f (Cx)

Vertical Dilation- Vertical dilation is the stretching of a function to increase the distance from f(x) to the x-axis by a factor.

The dilation transformation of a function y=f(x) is a function that is vertically dilated by a scale factor C.

Y = C * f(x)

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Things to Remember

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• A dilation is a transformation that enlarges or contracts the size of a figure. This means that the pre-image and image are similar and are scaled up or down using a scale factor. The original figure is stretched or shrunk as a result of dilation.
• The scale factor is the number multiplied by each coordinate to produce the new image.
• The dilation centre is a fixed point in the plane.
• The scale factor equals the length of the scale diagram divided by the length of the original diagram.
• If the scale factor is greater than one, the image will stretch.
• The image shrinks if the scale factor is between 0 and 1.
• If the scale factor is 1, the original and produced images are congruent.
• Horizontal dilation is the process of stretching a function so that the distance from f(x) to the y-axis increases by a factor.
• Vertical dilation is the process of stretching a function so that the distance between f(x) and the x-axis increases by a factor.

Read More: Cartesian System

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