Which Graph Shows A Dilation

Which Graph Shows A Dilation

A dilation is a transformation in which an object is enlarged or reduced in size, while maintaining its shape and proportionality. It is a type of similarity transformation, which means that the resulting figure is similar to the original figure, but with a different size. Dilations are commonly used in geometry to resize objects, such as maps, blueprints, and drawings. In this article, we will discuss the graph that shows a dilation, including its properties, examples, and applications.

What is a Dilation?

A dilation is a transformation that changes the size of a figure but not its shape. It is similar to a zoom function on a camera, where the image is enlarged or reduced but remains in proportion. The scale factor of a dilation is a ratio that represents the amount of enlargement or reduction of the figure. For example, if the scale factor is 2, the figure is enlarged by a factor of 2, and if the scale factor is 0.5, the figure is reduced by a factor of 2.

Dilations can be performed in two-dimensional and three-dimensional spaces, and they can be centered at any point. When a dilation is centered at the origin, it is called a central dilation, and when it is centered at a point other than the origin, it is called a non-central dilation.

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Graphical Representation of A Dilation:

Dilations can be represented graphically on a coordinate plane. In a two-dimensional space, a dilation can be performed by multiplying the coordinates of each point by the scale factor. For example, if the coordinates of a point are (x, y), and the scale factor is k, the coordinates of the dilated point will be (kx, ky). This means that the point will move away from the origin if k is greater than 1 and move towards the origin if k is less than 1.

Properties of A Dilation:

A dilation can be described by its scale factor, which is the ratio of the size of the resulting figure to the size of the original figure. The scale factor is always a positive number, and it can be greater than or less than one, depending on whether the object is enlarged or reduced. If the scale factor is greater than one, the object is enlarged, and if the scale factor is less than one, the object is reduced. The center of dilation is a fixed point around which the object is enlarged or reduced, and it is usually denoted by a dot or a letter.

Graph of A Dilation:

The graph of a dilation shows the original figure and the resulting figure after the dilation. The original figure is usually drawn in blue, and the resulting figure is drawn in red. The center of dilation is marked by a point, usually denoted by the letter "O." The scale factor is indicated by a number, usually written near the center of dilation. The graph also shows the direction and degree of the enlargement or reduction, which is indicated by the arrow and the angle of rotation.

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Conclusion:

In summary, a dilation is a transformation that changes the size of a figure but not its shape. It can be represented graphically on a coordinate plane by multiplying the coordinates of each point by the scale factor. When a dilation is performed, the size of the figure is changed, but the shape is preserved. Dilations are used in many fields of study and can be centered at any point. The scale factor of a dilation can be greater than 1 or less than 1, depending on whether the figure is being enlarged or reduced. Dilations are an important concept in mathematics and can help us to understand the properties of geometric figures.